Question
Find the area of an isosceles triangle whose one side is 10 cm greater than each of its equal sides and perimeter is 100 cm.
Hint:
Let two equal sides be x cm
The correct answer is: 200√5 cm2
It is given that one side is 10 cm greater than each of its equal sides.
Let two equal sides be x cm
So, third side = x + 10
Perimeter = 100 cm.
i.e. Sum of all sides = 100
x + x + x + 10 = 100
3x = 90. ⇒ x = 30 cm
Two equal sides = 30 cm
Third side = 30 + 10 = 40 cm
Using Heron’s formula,
Area of triangle =
where s = ![fraction numerator a plus b plus c over denominator 2 end fraction](data:image/png;base64,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)
s =
= 50
Area of triangle = ![square root of 50 left parenthesis 50 minus 30 right parenthesis left parenthesis 50 minus 30 right parenthesis left parenthesis 50 minus 40 right parenthesis end root](data:image/png;base64,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)
= ![square root of 50 left parenthesis 20 right parenthesis left parenthesis 20 right parenthesis left parenthesis 10 right parenthesis end root](data:image/png;base64,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)
= ![square root of 200000](data:image/png;base64,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)
= ![200 square root of 5 cm squared](data:image/png;base64,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)
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A Cylinder tank has a diameter 75 cm and height 1.8 m, Find the capacity in litres to three significant figures.
A Cylinder tank has a diameter 75 cm and height 1.8 m, Find the capacity in litres to three significant figures.
Identify the line having y-intercept = ![1 half](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABIAAAAjCAYAAACZ6FpfAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAXQ/cXWQAAAJFJREFUeNpjYMAP1IC4FogvMFAIFgNxGhD/Z6ASGDVo1KBBYdB/LHgUDCbwn0w8CgYLsAbiNUD8CYh/QaujaHIMOgjEkUDMA+VrAfFRqBjFQB6IL1HLyz+oYYgl1HsUAQ4gPgmNBLKBIBBvAGI3SgxRghqiQokhGkA8G4i5KDFEHIhXATELpYG7BeoimhZyWAEAI3M1I31CbrEAAABidEVYdE1hdGhNTAA8bWF0aCB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMTk5OC9NYXRoL01hdGhNTCI+PG1mcmFjPjxtbj4xPC9tbj48bW4+MjwvbW4+PC9tZnJhYz48L21hdGg+ND6jrQAAAABJRU5ErkJggg==)
Identify the line having y-intercept = ![1 half](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABIAAAAjCAYAAACZ6FpfAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAXQ/cXWQAAAJFJREFUeNpjYMAP1IC4FogvMFAIFgNxGhD/Z6ASGDVo1KBBYdB/LHgUDCbwn0w8CgYLsAbiNUD8CYh/QaujaHIMOgjEkUDMA+VrAfFRqBjFQB6IL1HLyz+oYYgl1HsUAQ4gPgmNBLKBIBBvAGI3SgxRghqiQokhGkA8G4i5KDFEHIhXATELpYG7BeoimhZyWAEAI3M1I31CbrEAAABidEVYdE1hdGhNTAA8bWF0aCB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMTk5OC9NYXRoL01hdGhNTCI+PG1mcmFjPjxtbj4xPC9tbj48bW4+MjwvbW4+PC9tZnJhYz48L21hdGg+ND6jrQAAAABJRU5ErkJggg==)
Find the perimeter and height of an equilateral triangle whose area is equal to 60
cm2
Find the perimeter and height of an equilateral triangle whose area is equal to 60
cm2
A ground in a shape of a parallelogram needs to be fenced by a wire. The one side of the parallelogram is 8 inches and the area of ground is 120 sq. inches respectively.
Find the minimum length of wire needed for the work.
A ground in a shape of a parallelogram needs to be fenced by a wire. The one side of the parallelogram is 8 inches and the area of ground is 120 sq. inches respectively.
Find the minimum length of wire needed for the work.
Identify the line having slope 2.
Identify the line having slope 2.
Find equation of a line parallel to line with an equation y = 5x + 1 and passing through (1, 10).
Find equation of a line parallel to line with an equation y = 5x + 1 and passing through (1, 10).
In the figure given below, find the area of:
(i) the shaded portion and (ii) the unshaded portion.
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAboAAAEsCAYAAAC1yHbbAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAAFxEAABcRAcom8z8AAEJ+SURBVHhe7Z0FeBTHH4apC1DgT1uguGtxCO4SXIu1eJFCaaG4U9zd3a24Fy0OxV1DgKARQkhCPN9/f9O7kIRDQhKYPb73eb4nydzu3d7tZt+b2ZnZOCCEEELskNDQUAQFBSGOv78/zp07h/Pnz6ufkjNnzqicPn1a5dSpUwzDMAxjmhw/fhyurq4IDAxEnDt37iBTpkxInjw5UqZMqZIiRQqGYRiGMW2SJUuGzZs3q1pdnHv37iF16tSIEycOwzAMw9hF4saNi3Xr1sHb2xtx7t69i7Rp09pckGEYhmHMmPjx42PZsmW4f/8+4ri4uFB0DMMwjF0lXrx4mDNnDq5du4Y4t2/fRpo0aSIsMGHCBPz1118MwzAMY4osWrQICRIkCPOYNF1OmjRJdUyJc+vWredEJ1U9QgghxEwkTZo0zGNffvklRo8ejcOHD9sW3eXLly2rEUIIIfrz5MkTfPvttxFEN3ToUOzZs4eiI4QQYn5siW7w4MHYuXMn4ty8eZOiI4QQYmpsiW7gwIHYvn07RUcIIcT8UHSEEELsGlui+/PPP/H3339TdIQQQswPRUcIIcSuoegIIYTYNRQdIYQQu4aiI4QQYtdQdIQQQuwaio4QQohdQ9ERQgixayg6Qgghdg1FRwghxK6h6AjRjFDLT0JIzEDRERJjeMHL5SiObFiJlYuXY/maQzh44wm8LY/+Ryj83S7g9L71WL1yBZYvX44VK5Zh2eJVWLP/Ai57h1J0hMQwFB0hMUGwDx6dXYDl05ujdaWiKJ4rB7KmLQGH1lMw5dxDPLIsZvzLwWlVc/xQNCm+y5QXhQoXhoNDfuTLUQrlu8zH0jvUHCExDUVHSEzgfRkHRrVFzxnzseLfMzhzcje2jaqIQt8lwzcNJmHh9aeWBW/g0GAH5CzliPqzDuL0mdM4ffoUTp04i3M3HsA1gE2XhMQ0FB0hMUGIH7xd78PVOwjBliL4LsaYkv9D/C+rouGKK3ioCq/j4KCiyF/rZ3Q7bJVfFAn0hre7K1xd3eHu7Q9/SzFCAhHg64unwYYqje3xf2w87vYInk9Dnskz6Akee7jB1dNYLsRSRoidQ9ERElsEbcSsaimQ5NNyqL3gPO6qQiccGlIMBWq1RNcDEa/evZoQBHn+g13jG6BRzizInqsg8rYahYE7ruNOoCHYOyswvVY51By7Apu2j8SUxg4okiUfcrabjoU3vPDY/QSOLW2J+o5ZkaZ4YzRYdBTHvcNJkBA7haIjJLYIXIMplZLh61Q/ov1WF/iowuvY/2dB5KpYD63WO+HBgwe4/+ARHhnVq7Ca4AsIfbQPa0ZXRokmHdB1+kqs27QS8yf2R8+287D2pge87szAoPRxkSBzOZQbPAsLN6/FpiW90L5BXuRp1Qo//TgIA8fOw8LtK7BoWE04lG6EpgsvwNny/ITYKxQdIbFCCPzP9kDTHMmRuO5EzHUOsJTfwOHhpeCQJjGSFKyIWrWqolKNtvh51FZsdvGGn2Wp53mEO+vbolb+kigx7TguWqwY6n4RF3acxZXHT/DkzkwMyZMIiQu0Quddt3FfLXEfl+cUQ9rs+ZGrzV9Ye8kXaktcJ6GbQw5kb74Iqx6rBQmxWyg6QmKDwMPY2DETkn5XEuXnnMLlsOthXnhwcj1WTRqIP/v2Qe9e3dC1Y0PULl4U5duNxewbL7huF3oWewcWQcaMHdDtxGNL7TA8fvBznoIBhb9BkqZzsN3dUgx/uG9vhAK5qqHuSifcsZQiwKhtVsmMVBUHYfTlQEshIfYJRUdIjHMftzfWQ6mkKZCu9UKsuf/0Fc2St3FtqiPK5XZA4eFHcNNSGoGn+7D812xIkrMb+p59DF9L8TMsoitkiK75TGx9YH3FJ7i38Qfky10LDZdewS1LKXxWYnylNEhcuheGnnv+2QixJyg6QmIUHzw+3g+/lEiLpDVGYuq1py9pjgzHzYnoWiU7kladjpW2vOO5FdN+/A5f5OiKPue88Hy9L5zomonogizlVtHVRIMllyOKzjEtvinbB8PPv2HvT0JMAkUXTUJCQhAayn5rRAiE3/UZGFsnCxIV6Yiexx+/nuQMgs8PQvuKmZGi0QJssV7OC0/AYazrmAPJMnZA15NeL6/RUXSxRlBQkAoxFxTdG3LmzBksWLAAx44dU7IjJNh1C9Z0LYX8Rdug9ba78LSUR+DRGRy5cAGnwz8YfAUnR9dA2dLVUG3+BXhYiiPiiht/NYFj1uIoNf0krlpaJkM8LuPSngu45uUNH5dpGFjo69cTnfdyjK2YBonL9qXoooCcE+X/fvfu3fD2jurwEPKuoOiiyO3bt7F+/XpUq1YNCRIkwNixYy2PkPeaEGecmlICReImQryqAzF+214c3LEVmzdtxMZNm7Dp2DXcluqd01QMmdQJ7aaswOqNf+PvbeuwamlntK9SBVXaLsDiey+qLYQi5M5qzOpQEHnrtcNvczdgy451WDqlP3q1noPVzh7wujcV/XLGRYIGU7Dx/jPR3V1bFVkyVkTN+RefDSXwW41JZZMiQZE/8OdZiu51OXDgALJmzaoi//vnzp2Dn9/r1tvJu4Kie03c3Nywfft2NGrUCPHjx1efxUcffYRJkyZZliDvNUHHsLVnGZTMkQWZ8jigcCEHFCxQAAXy5EKuXHmRu9NMrFUjxq/i0oE/MbhpGZTPkQu5czogf6NO+HnlMRx++OqWgeCH67F6SFWUy5MD3+crBodfxmHYnlv/zbriboiwSSmUGbAWh8OGDATA80BXNKzXCT22uRj1QisXsLd7DdRpMwpzb7JF4nU5evQoMmTIoP7/P//8c+TJkweTJ09WNT02aeoLRfcKHj16hH/++Qc//fRTmOCskQ9r/Pjx8JVpl54+VT+Z9zUytZa78YXIFa4P7uHunTu4Y42LC1xcPeDpbSz31A9+vo/h5XoP96T8zl3cffgI7k/94R9g5Gnk5w0XWcbfWN/LDa53XYznNtZ198Jjo0bhZxx/T32ewOuRBzweP4FP+PW8PeHxyNN4fZ8Iz+fz2NgmT2NbfMIty7wwUnPbu3evqs2FPw98+umnyJs3L2bOnKn2d3Dwq4b+k7cNRWeDwMBANWOFNFM0a9YMyZIlU7W38J+D5JNPPkGVKlXUBzZo0CAMHDiQeW8zGEOGjcCIkaMwatRIjBwlP8Nl+FAMGSTLDcKgwcMwbISxrHpsJEaNGIbhQwZjsM3njZwhGDJ0hOX5jdcZPgxDB1seGzQEQ4cbZcOMZdRr/Rd5veHGawwbbLx22PMYryfbK+uHW5Z5cUYY+6x169b45ptvnjsXSORSRrFixTB79mxVw/Py8mJHNU2g6Gzg5OSE3377DenSpVPf1sK///D54IMP1AeWKFEihnmrSWij7L8kfMljTHTyv//9T7XqfPjhhzbPB9YkSZIE5cuXx4oVK9SXZvLuoehscPXqVTRu3BifffZZhPceOSI6hmHer9g6F4SPLJM9e3YsW7aM1+00gaKzgbTHnz17FnPnzkWFChVsNltKpOmyUqVK6Nu3LwYMGID+/fszDGOH6devH4YMGYKWLVvi66+/tnk+kGTOnFktK9fyXF1d2XSpCRTdK7hy5QqmT5+OcuXKRfgcJPJhjRs3TnVEkSYKf3/pLMAwjD1Gxsvu27cPWbJkee5cIJc5evTogf379yMgwNaIf/IuoeheE6nhybiZMmXKhH0W0r14ypQpliUIIfbOv//+G0F06dOnR8eOHbFt2zb4+Dw/1TbRA4ouCkgzhIyjkR5YBQsWVB1VRo8ezeYJQt4TpEYntbfUqVOrHpirVq2Cp6fNOXCIRlB0b4A0Tcg3uD/++AObNm3iFGCEvCdcuHBBNVHKEIKHD9UwfWICKLpoID2qZBApB4gS8n4g1+pkjku24pgLio4QE3H//n0cOnQIt27d4smWkNeEoiOmQWaakPlGd+3aFeHC/+PHj9UBu2fPHtUD1p4ZOXKk+j9s3749ByMT8ppQdMQ0yC2R4saNq6ZgunjxoqUUOHjwoOoBK1O1Xbt2zVJqnwwbNkz9H7Zp00Y1oxFzIcOVZHyuzIspkd937tzJfRnLUHTENEiP18SJEyNFihQ4f/68pRRq7FLChAlVTziZ1caeGT58uPo//OWXX3hyNCFDhw6NcD6VyNRi3bt35/CEWISiI6ZBxjDJrBQpU6Z8rkYncxHKsUrREZ2RWVZk/8nwpKlTp6JLly7qpCvThskXNhI7vBeikxNCp06dUKtWLXTt2lVN8UXMh1V0qVKlUhNvW5EmTflWTNER3ZGpAmX/yVRiggxNKlu2rCpbvHixKiMxz3shOvmmJNd2ZPtl9nG5vxwxHyI6uQ4nA/Vz5MiB/Pnzq8hMFTIfacaMGWNGdKEh6gT0LKGQDo469HGk6MyNVXQ//vij+vvSpUtqAmi5xY/MvkRih/dCdNI8ILfWqFGjhnoPffr0sTxCzISI7rvvvotwPIZPpkyZoiW6AJeNWDSgNqpXrgzHSlVQpUolOJaugqq/jMe0S0+gQzsARWduZFYlaaaUL97SMiHXnGV/ykTQHC4Se9i96GRwp9wMUToqyGwm8h6KFi3KWQ1MiIhOelwmT55c1dJlH0o2btyoOqOkTZs2GqLzh/uOdqhTIBGSVfkFf/T7EwMH9EOf7v3Qf9JabHZ5aizx7qHozI1VdHILMJGcHM/yu3yBW7duHWUXS9i96Hbv3q0OqA4dOqi7hufOnVtdz5EuvcRchL9GF34YgZRH/xqdF+6sboQKJYujxmoXeMr5xjjpyInHeu7R4RRkHV7Qtm1bis6EWJsuGzZsqKYSlHGfUpuTFqfvv/+ePS9jCbsWnZykrL2cpGeeILfVkb8HDx6s/ibmQYRmHV4gcw5aiZnhBU9wf20TVC5VFNWWXMbjKFstEP43/sb26aMwauhwDFvwNzY7S3NnKILd/8U/azdj85n7eHBnH7bNMR4fPgczd97ATbXuI7geX4jF40dgxNwt2HrLB36q/HmkRiDHb/PmzSk6ExK5M4ogX8al17A0Z8rkByTmsWvRSbNWqVKl1HbLjBILFy7Er7/+qv6uUqUKZx03GUeOHMHHH3+Mr776KsI4OplRXpqDpFYnA3LfjP9EV6l8GdTd5GYpe10C4X1zFsZ0dUTV0qVRoXIllG/UHHU7LsSGGw/x4ExXNMqRA0nL9Ee3mb3RqVVFOBbJg6xl2qPzjDVYs3UiRg1pgrb1iqJwsWLI320qlty0fU8zmRlG7n4vd6/mZOLmw/rFu0iRIup8JHF0dFRl9erV473sYgm7Fp3c5dd6sTdypG2cvS/Nxb1791RNXL60uLu7W0oBFxcXDBo0SN0y6dGjR5bSqPIYd1bVR+mMSZG22WCMnTEDM2cvx9Jd13HlpeeeIAR77MTCtrmQtvEwjL/ga5QYuP6DLQPmYO1JF9y60Bc/O6RHnKSNUHfZaThJbfHRKixqlge5E6dEprb9MfT4Y6P25wWP7W1Ro2ReFJ9yDg/keYhdIXcpt3U+qlChAk6fPm1ZisQ0di06OfHJNsv4OfndmtLGt24pl4OOF3/Jf/jA7cgY9KtZCAUdCqNI8SIoXLgI8pZpiZZTt2Cvu/9/AnuOR3h8qCNqpC+OcjPP4EpYJSsYQT5+CAz2w5MT3dA4Xxp8WX8W1oV52Bnnp1RE/vyl8cOamwhrW7g5Db2rZcJ39ZdhmyFYHp32hbRETJgwIexcNGbMGFU7ly9xJPawW9G5urqiePHiiBcvnprtPTyLFi1S70W+RYWvGZD3mRAE+3nC3cUJTlcu4eLFCzh/dhvW9ymFMtkdUHH6MVy3dUksxAXOf9VA9hS10HjjbTx/ujJEd6wLfsqXAd+0XYX91nmYQ2/hwoyqKFi+Ftru87YUSvFs/FklFeKVGo/5HqHGVhFCoovdik7mRZRBxHKNTqQXnpMnT6qeezLw+Ny5c5ZSQmxwbxFG1kmDJI4TMPeO//PiCbiKE5OLIul3NfDTptu4ayl+hiG6413QJF9GfPvzCuy23lwh9AbOTqmMAmVroM1uD0uhUew8E/0rpTBENw5z3Sg6QmICuxWdjJ87deqUun4TuXlSbm9y/fp19TinAyMvxX8P5rdOi0Q5u6DPuSd47sY4/ldxfHJhJE1aDY0M0d23FD/DH95KdBkM0S1/XnRlaqD1rsiiS4n4pY0anTtFR0hMYNfX6Ah5bUIC4Of3FL4RzBKK0OvT0bd2WqRuMg9r7wc9f80s1B2uu9ugQsrCKCvX6CzFqinUxxd+AT7wPGYV3TLsChOdE85YRbcznOhuzEA/R6NGR9EREmNQdIQI3kewdctEDN1/G3ceP8ETLy94ee7H7j9roGLhpmi+5RZe2J/TcwtmNc6BLE1GYOJpN3jKunf3Ysvghdh0/iEeXO6PNgUzIkmbNTgQbFkHd3FlZlU4lKuNX/Y/u0aHe/MwqGoqfFV2KpY8sZQRQqLFey86adaU8UgyfkUizZrM+5YgBHmfwZFtHdH+92Zo8WMzNG/aBD+1/gk1/+iPXrOO44J3EIKDAhFga93gJ/A4MRqDf3dE+Vo/oEHTpmjcoSN+7rMKO+49hvflfmhVIBO+NUS3/2kwQoKDjedy+U905Q3RHfBEYLDx/FLu+Rem/Pg9kpaZjMUegQgKMp7/uddkdI+cS2TfRaVXN3uAxx6s0RnIvc1k4me5hU+3bt2Y9yrd0a17T/Ts2gEdWxZDiTQf4cOw4z0RvijVEHU79sCffXqiV/fu6Gpj/e49eqNf71ZoUTYpEn9gWffLdEhTvTXa9jSev7kDciRJhC9zVkf9Tr2MZXuhd8/WaF4+HZKmzohc9Tuge2/j+Xv1Qe+OdVApZzJ8lbIMKv3aHT17GtvWPfJrMrpHzicyeXxUe3XfunULct4lMQtFZyCTqYZ/jwzDMNGNzNYTlZl6pHe43Gl84sSJlhISU1B0Bps2bYrwHhmGYaIbmZIu/OTjr0JuvCpzXsr4Xg4gj1koOoPIokuaNClatGiB9u3bo3Xr1oyGkX3TpEkTdSNd2WdyqxO5HZPMglO1alVTp3bt2siTJ0/Y8ZgyZUq0adNG3bHA1mfBvPvI3VFkrsovvvgibL9FRXQyzEkm6pb15JieN2+e5RESE1B0BpFFJydMGX8ns8PLAcjoF9k3cj3DenzK3QtmzpypxkbKHKdmjUxQfebMGfTu3TvseKxYsaKa1V5u6WLrs2DefaTzyfHjx5EkSZKw/RYV0W3evBmZM2cOW7dBgwactSkGoegMIouuRIkS8PB4NraJ6IlM4Cw3W5V9JqKTb8Fy+57Dhw+bNnKHBvkfs85yL6lUqRLvVGACpFObtAZZ91tURCe1dbknnXVdOSmvXLnS8iiJLhSdga0andykleiN3IbJenwmSJAA06dPV9+q5f5ee/bsMW2kVtqrV6+w41FqdLz3nP6cPXv2jWp0cq/MHDlyhK1nzc8//6xO0CT6UHQGFJ05iSy6GTNm4MSJE0oWcgsms0Zu10LRmY83EZ3U1Dt37qx6aFrXs0ZaK6RHOIk+FJ0BRWdOKDqiE28iOmmByJs3b9g6kSM3ivbx8bEsTd4Uis6AojMnFB3RiaiKTmZOkUHln3zySdg6kZM9e3asX7/esgZ5Uyg6A4rOnFB0RCeiKjrpXVuoUKGw5V8U6aji5+dnWYu8CRSdAUVnTig6ohNREZ3U5qZNm4asWbOqnprp0qULGxMq1+u+/vprdY1OTs7VqlVTTZzkzaHoDCg6c0LREZ2IiuhkAm/Zz3LukZOt9BSuXLmyWi9evHhqvkwp27p1K3bt2sX5L6MJRWdA0ZkTio7oxJt0RglPu3bt1HqJEyfG6tWrLaUkJqDoDCg6c0LREZ2IruhatWoVtt6SJUsspSQmoOgMKDpzQtERnYhJ0ckEzyTmoOgMKDpzQtERnaDo9IWiM6DozAlFR3SCotMXis6AojMnFB3RCYpOXyg6A4rOnFB0RCcoOn2h6AwoOnNC0RGdoOj0haIzoOjMCUVHdIKi0xeKzoCiMycUHdEJik5fKDoDis6cUHREJyg6faHoDCg6c0LREZ2g6PSFojOg6MwJRUd0gqLTF4rOgKIzJxQd0QmKTl8oOgOKzpxQdEQnKDp9oegMKDpzQtERnaDo9IWiM6DozAlFR3SCotMXis6AojMnFB3RCYpOXyg6A4rOnFB0RCcoOn2h6AwoOnNC0RGdoOj0haIzoOjMCUVHdIKi0xeKzoCiMycUHdEJik5fKDoDis6cUHREJyg6faHoDCg6c0LREZ2g6PSFojOg6MwJRUd0gqLTF4rOgKIzJxQd0QmKTl8oOgOKzpxQdEQnKDp9oegMKDpzQtERnaDo9IWiM6DozAlFR3SCotMXis6AojMnFB3RCYpOXyg6A4rOnFB0RCcoOn2h6AwoOnNC0RGdoOj0haIzoOjMCUVHdIKi0xeKzoCiMycUHdEJik5fKDoDis6cUHREJyg6faHoDCg6c0LREZ2g6PSFojOg6MwJRUd0gqLTF4rOgKIzJxQd0QlbonNyclKPrV69Gk2bNkWTJk3QuHFjlZEjR6rHrFB0sQdFZ0DRmROKjuiELdE5Ozurx3799dewcmtKliypHrNC0cUeFJ0BRWdOKDqiEy8T3R9//KHKxo8fr5aTWB+zQtHFHhSdAUVnTig6ohMvE13nzp1V2V9//YWAgAAEBgaq8vBQdLGHXYrO09NTXQS2Rg62R48eWR59HorOnFB0RCdeR3QffPCBijy2ZcsW9ZgVii72sEvRde3aFR9++GHYNn/66aeoWrUqDh06ZFkiIhSdOaHoiE68jujSp0+PvHnzolSpUjhw4IB6zApFF3vYnehCQkJQq1Ytta1ZsmRB5cqVkS5dOvV3rly5cOvWLcuSz6DozAlFR3TidUS3efNm9bctKLrYwy5FV7NmTbWtU6ZMUWXHjh1D0qRJVS1v7dq1qiw8FJ05oeiITryO6OTYfBEUXexh1zW6UaNGWUqBggULqrL58+dbSp5B0ZkTio7oxMtEZ+112aBBAwwYMEAlsswoutjDrkVnrdEdPXoUX3/9NT766CPs2LFDlYWHojMnFB3RiZeJrmPHjmHl1nz//ffqMSsUXexhl6KrW7eu2tZs2bKpTigZMmRQf4sAfXx8LEs+w5boXF1dLY8SXXFzc3tvRGerOzrRi/Pnzz8nuuvXr6vHLl26pC6bhE/kznEUXexhl6L74YcfImxzvHjx0K5dO9y+fduyVEQii056RLm7u1seJboi+yht2rRqn9mz6KRDFUWnPxcuXECyZMnC9psIi3Nd6oFdiq527dpqW7t166a298aNG/D19bUs8TyRRZcyZUrVpt6nTx/06NGD0TCyb37//XclONlnCRMmtFvRSa9hec9SFvlzYPRI3759lajixo0btt8oOn2wS9FZe13KdDuvQ3jRyWBO+Sk9NJl3G+vgWluxPm7db/YsuvDHY/j3z+gTuf4vP8PvM4pOH+xSdJUqVVLbOnToUEvpy4lco2PMl48//hhTp07FqVOnTC+6M2fOqNYIW++TMU8oOn2wO9GFhoZixIgR6rrGxo0bLaUvh6LTL1988YUaElKoUCEUKFDghZFlcufOjRIlSqiTw7///mt60cm4z7Fjx6r3lSdPngjvt0iRImoiBFufGaNXKDp9sDvRvQmRmy6lnV1mUcmXL5860TBvN3KCl/t2yRRJMjRk//79r5W9e/faFIcZI+/F1ns8efIkli5dqm7xYuuzY95N8ufPr3p5S8uC9VxC0ekDRWcQuUaXPXt2rFu3Tp1w5INg3m62bt2qxjsePHjwtSNSfJnoZBm5fifXvyTyu3TvtrVsTEa2SWpo1teVSPOq1Dxlm22tI9m3b99z71Ei2yzC27Ztm4qtz495+5F9Mnv2bHWt2Hoeoej0gaIziCw6qc3JCUqulUiNgnm7EQnICV2aIF+nGfJly8h+lOeTWpDc/FLGWErk90WLFil5vEyQ0YnISoQtvfJkyIv1tX/88Uf0799ffZk6cuRIlJpaZVnZXuvnFPmzY95NZGiB3IJHJGU9j1B0+kDRGUQWncxYILWK8Cdb5u3H1ok+qhGRyXRLmTNnjrCPJZkyZVIdluTbeGzITl57w4YN6nUiv7Zcg5RZ7CdNmqSEZWv9l8XW58W8u8g+XLhwIRIlShS2jyk6faDoDGyJTpqFDh8+bPMkw5gjsv9mzZoVNoi3evXqGDlyJIYPH65mv5EymclCanYva0Z804jo1q9fr0Qn3c+bN2+O6dOnqx6VVvGK7NasWaOWtfUcjDkizdNyHFF0ekLRGVB09hfrNS7rdHAy243cIkWuzR0/flw1G1p7L8qsObFRqwsvOumkIJOMX7lyRX37nzdvnvrfks5P3bt3V9tl6zkYc4Si0xuKzoCis7+IZGR4iXTJl30q18mkKVpkJhGxWKeKq1ChghKjxNZzvWkii27QoEFKslJ7lEjPUnl9meBAtklka+t5GP1D0ekNRWdA0dlfZN8tW7YsrNY2c+bMCNfCpAOBNCXKY2XLln2ropPXEdFJhxh5/WrVqmH37t0UnYlD0ekNRWdA0dlfrKLLmjWr2qfS6UPkZn1cTkxW0ZUuXfqdiK5Dhw7q9eXaoXRooOjMG4pObyg6A4rO/iKSkR6P1qZLuR+YtelSRCPCqVKlinpMbt/0NkVnHQtnvW+iDDeQYy2mrxEyby8Und5QdAYUnf1FpCFj1Kx3spBZblatWqXGO8nsIjLhtxz4MhHvmDFjYr3XpYhOpvWSO2nIaw0cOFANLv7ss88wZMgQdkYxeSg6vaHoDCg6+4xck5O7zFsPcKndNW3aFPXr1w8bclCkSBF1fUykZOs5opPwopPelTIfZ8uWLdU8rNbbC4mIt2/fzmZLk4ei0xuKzoCis9+IbGTcnNTowu9jOZlIbS59+vQYPXq0qmXFdNOhvLb0/MyZM2eE15bIPQ8bN26sHpfjTK7R2XoOxhyh6PSGojOg6Ow3Ii8RjkzPNGHCBCU9aapcsGBBWGcUObHI79LUGZOyk+fatWuXGrQur2uNiFVeXx6zzr5ja33GPKHo9IaiM6Do7DsiHBGKnIysA8bld2mylDtDS61ObgckTZ0xXauT55PenvK61sjri1TZXGk/oej0hqIzoOjez0hzpfS0lFlSZBqumJYc8/6EotMbis6Aont/I6KT2l5sdEZh3p9QdHpD0RlQdAzDRCcUnd5QdAYUHcMw0QlFpzcUnQFFxzBMdELR6Q1FZ0DRMQwTnVB0ekPRGVB0DMNEJxSd3lB0BhQdwzDRybsRnSseHlqCxbP+wtqrnvAOtRQrfPH4xiasmDYMA3v3Qd8+fdCnVw/06N0P/f86hPOeIZbl3g8oOgOKjmGY6OTtis4HPg/2YM/CdmhVOCESpi4Gx+VXcS/Y8rAQ4ozT88oiR4pUSJ6vIqrWqYWaVRxRsVpN1Bq7EQcfUnQUHUXHMEwU8vZEFwCvKxuwomdV1CyZAqkTfYA4SYqgnCG6B+FF538OO4bkRYpcrdBhyzXcdX2Ihw8e4MED46eXL/yDLMu9J+glutAA+Hs64/KZ4zh25IgSjcqRf3Hilge8Y2nnUHQMw0Qnb090d3F12VB0r9oDvZbPw8rBZZE1eSlUXH4lYo1ORDesMNI7dEKvk96WwqjgB3+Py7h8QiZTOIETlx/igZ/1ITfcu3UDt9x9EPTUBbcvHcXho6dwyuWJUdcUghHkegmXjHP4kePOcH4SaJS8W/QSnf95HJ5eGum++Q7JM2VFdkM432fLhqy5CqLk6J04+yR2qtsUHcMw0cnbE10wgv2ewtfH+AlnXJlTGdmTlUCFZZFFdx47hxdBhkJd0fes1VCvy1N4XliMBT3LoEKhbPg+e1E41OiGzltP4ox/KIIvTUTXnwqiSLeZWLq6O3q3yIVsWbIhQ+NhGHnUCTevrsH6cfXQMHcWZExXDY5DtmCXewDeZSVSL9F5/oMVXbIhYd6uGHzgEq7edMaNq1dx5ZoTnNx84BdLzcrbNkcUXa6cObFrx3YcoegYhnmNvJvOKDdwaaYjstoU3Tn8PfB7fJexLprM/Qf/njyJE6ev4aqbv1FXexmhCLw7B2MbVUTR+sMx4eRV3HU+hxN/9Ub/WZMx654/Ai6OR7ea8RCn8I+oPGItdly/jKvHp2Fo87xImc0R5Zr8hD/W78eZa+fx79yGqJCjEmouPour77Bap5no9mBJ55xIUnYiFrlayqJEIAIfu8DF6QouX7mFmw994Ss9kYyE+D3GIw9PePkFIDTAFQ9uXcGVG3dh7Hds2r49wnvM8X1ObNm+A0ePHrF5UDMMw4TPuxHddVyc8QLRBVzHwSklkCddciTPXAAORQqjQP6qcOw3FzMuuMHzhdUrV1yYVgmlytVCw2VO8LCUwtcFd++74F5QMPwujUeXsl8jfuWRGHnBB8Yp1OAGzk+rgKyJS6DEhO04au0Cem8W+pdLi4ydl+Lvd9gBRrsa3bIuuZCk9DjMvRfVdl1jB9zbjI2j6qB+hUJwKNgAdbotxPyrHpAWaq9j4zCgdyd0Wfg3Tu4biJ5NHZC/fH38vOAIOi3ZiA8+ePYek6TIgG6j52Pr/oPYu9f2gc0wDGONdqIL8YXnrUPYvX0tVi5bhuVLFmPh5PZo2zg/cjYbjomnHyPAsmhETmBDs6zIVr49+p/7T2ERCcXTi2PQsVhypG64Apt9LcW4ixtL6qFYujr4cbsr3C2l8FiNCbVSImWdUZh77aml8O2jneiWSo2u9HjMd7OUvRbGNwWP9ZjXsgrKNmiPzlMnYOL4CRjXpwkaz1qCrcbO8NreEnVK/w8fl2mNVmMnYe6y8Rjbuy5q1a6Mrwv+ZIjug7D3+PnHX6JgnvoYMH8rdu/fh/2UHcMwL4l2orPJbTitb4DKWYqhyIiDuGKrghWwHtOqZEDK0j0w+LytRk6L6IqnRJoGS7HBy/okt3B1fh0USV8XTba44IGlNNR9OcZUNkRXeRimXfqvq8q7QC/RPTJqdJ2MjfkyHTKXdkSlajVQo143dF59GqfCvjnYINAJF+c6omDB2mi2xtXS88fA9SAOnj2La/4h8NjVEc1KJUeC6sMx7KyvtGYa7MSGHkWRJE6yCO8x6cdxUCFdJpTpNhsbdu/DIUN2tg5uhmEYiTlEFwL/68PRLXdGfNt0Pnba8s6TxRhZIQ3+V6Yvhlx4mehSIHWDJc+LzqjRNd4cTnRuhuiqGKKrNgIzLr/sJB676CW6gPu4cXQ+powfieGDhmBQ/x7o2roKKvzgiPKjtmG/R6BFUBEJ9dqGVfXSIkWdP7H4oaUwAkG493d7NMifDVk7bMYxSylwHIemNEKeT5JHeI/p48VBw7xpkLH+ECz8+x8cPLgPe20c3AzDMJJ31Rnl8sxKhuhKouLya3hg6+QYgafwPNYRDTLnQcYuW3Ai0FIcnuCjWNs+JzI4tkfPY7ZMSNHFAqEIebQb20cUQpacTdB+++2wD/AZwQi8NxtjiqXCt7XHYnVY43B4gnB/uyG6AjmQo8Mm/GspRegR7JvQADk/SR3hPaYzRFc3exqkrtIPc7buwYGD+yk6hmFemLcluoguu4cbC6ogW7JSqLTuFp713/PHY5cD2DD/MA46+4Zdiwt124SNfXMjW+EWaLf1juq78Dx+uLemISoXLoSCA/fihPJYMAKcNuPvvduw61EgAi6PRcdi3yFlvcVYH15082qhUJpa+GmTVXTG+dttKUZW/A7JqwzHdIruZTzF08O/o3qyXMg3+iBOPVeb9oe/00j0yJ8ScWtPwZpXiC77rxtx1FKqRDf+xaJLW7U/5m6j6BiGeXneXo3uCdwvbsKaccMxfNAf+L2Gcd77JAlS1u6AHiMmY9qmS3AJ9ccj56WY0LojuvXsjcEjh2LYsIHo3b8lmjWri6Yz/8ahxy+p/hlCXNyrOspWqoufev+JkUOGY2DX1mg7Yx6Wugci6PIItM+bAF9Xn4/VXtbncVa1y1zfVkKd9bdx31KKR+swsfa3SFxxICZe4DW6l+CLJ/vaoGzSPMg/7hDOPCe6IATdm4dxldIiUZ1RWPGCpsv70nQZVdFVo+gYhnl13p7o3HF772j8WbMMSpcqi/KVqqF6jeqoVr4kSjrWQ/3hu3DKqMKFhtyG0z8TMKtrdVSvUBIlylZE+Q7jMWzrFVx7+qo2zlAEe+zGPxObo1XFYihetB7qdJqP2efd4G6sGnJnPeb0aonWY/biXzV+S3DFvV0j0KPNCIw77g5PSyn8LmH//A5oO2oNtt5++Qi+2EQj0fnBx90ZF065Phu7Ifgdwr5h+ZEmRxt02f8g4mNWAi7i+CgHZCxcH+12exlas+B1ERednXE/MBhuO39Fo4LfI0eHyKJriFyfRHyPIro62Sg6hmFeL2/1Gl1oCEKCgxEcbPy0esYoC5YyoyCCxsKWDX627GtjPFdIpNcxKRqJ7j5uHpqMHnV6Ytiiv7B+3RqsWb8E8yY1Q7MaDqg4bgeOhLUHR8YPTy+OwB8V8iFb/b4YsmoN1q5ZhqUjmqP5jPnYZNSYvXa0QPXMKZC8+RoctKyF0APYOawyMsRJHOE9po8fB7WzJkOycr0wi9foGIZ5Rd5NZxTyumgkugA89TBqWHM7oleDgnDImxPfFyyOQi2HoO+qozjj/aq50h7jwekpmPRzCZTNnQPff18dju2nYPK5+3gkjx4ejC71jGr84H9w5r8VDNGdwall3VA2o0OE95j1uy/RpUFZlGkxCguNGt3+A+x1yTDMi0PR6Y1m1+gCEOB9G3cuncDxY0dx9PgpnLruigevPaD+CZ7cPofzsu7R8zjn7AlPGVtiVLuDfR7g3k1nOD/0xn9PJ3VxPwR5u2HpnEUR3mOO7FmxbvUKbNq+Bzt37+HsKAzDvDQUnd6YoDNKDGCzfflZ4a5/dkV4j9/nyo3d/+zF2VPHsc/GQc0wDBM+FJ3evB+iewUbN26M8B7VbXq2bsWhQ7x7AcMwrw5FpzcUnQHvR8cwTHRC0ekNRWdA0TEME51QdHpD0RlQdPadffv24ejRo/j333/DIn8fOHDA5vKxGXnNI0eOhG2H/P4utoOJ2VB0ekPRGVB09pu9e/eqg3nu3LmYMWNGWObMmYMtW7YoycgyttaNychryPEkr7lgwQK1DTNnzlQnx61btyoZ21qPMUcoOr2h6AwoOvvNoUOHMHHiRCRMmDDCPpZUqVIFq1ativUalUjs4MGDmDZtGhwdHfHZZ5+FbUO8ePHUdvz1119qW22tz+gfik5vKDoDis5+I/tw2LBh6sD+9NNPUbFiRZQvXx5JkyZV+7p+/frYvXs39u/fb3P96EZqciK5SZMm4bvvvlOvmTFjRrUd5cqVQ44cOVRZv379cPLkSZvPwegfik5vKDoDis5+I/tw+PDhSnJJkiRRMjl//jwGDBiAuHHjIkuWLKrpMLZqdfL6a9asQaZMmdSxVblyZSxfvhynT5/G8ePHsXbtWnTq1Anz5s1jjc7Eoej0hqIzoOjsN+FFJwe6iE4k06VLF3zxxRcoUKCAOthjS3TS6UVqlHJcZc6cGStXrsSpU6dw4sQJtS1nz57F1atXVacUqVnaeg5G/1B0ekPRGVB09hur6ORamFwbK126NEqUKKFOJlKj69+/v2q2jI0OKXJtTgQqNTY5ruRanLyOXI+TpstSpUqp7ZGm1IULF/J4M3EoOr2h6AwoOvuNVXS2OqP88ssv6vpZbF2fE9HJc3fo0EG9XrVq1ZT4Zs+e/dy2DB06VNXybD0Po38oOr2h6AwoOvuNVXSff/45EidOrE5GjRo1Uvu5YMGC2LBhQ6xdG7N2ROnatat6vbJly2LXrl3qsaVLl6reoDlz5lSPUXTmDkWnNxSdAUVnv7GKTpot5UCXDiCyv3Pnzq32de/evZWMYqPpUiKDwidPnoyPPvpINZ+OHj1abYP8H+3ZswdFihRR2yHX8Sg684ai0xuKzoCis9+EF93XX3+tOnxIB5Cff/5Z7ev8+fOrfR1bzZciUflnqlq1qnq9ZMmSoXv37li2bBlGjRqFVKlSqfLBgwdzeIGJQ9HpDUVnQNHZb2QfSrOg7FepUYnopJYl18nix4+vyseOHauEZGv9mIj0qJQhBdL5xPqa4SPyk3F2crK0tT6jf14lOn9/f/VFRo4/a+TYlBOwFYou9qDoDCg6+410/pg/fz4qVaqkBodLc6G19taiRQvV63HMmDGq40hsNV9KRKQ7duxQ/1xSuxPplSlTBs2aNcPUqVPVtbvYfH0mdvMq0Tk7OyNv3rwRzjPSyiDHhRWKLvawW9F5eXmpMUvjx49X8wrK2KUXYUt0MohYOinIiZF5N7F1QnmTiNjk+lfkGpPU7KQ8Nmtz4SMylS9Pco1OXlci2yDHWVQlZ+vzYt5dZD/KEJEXiU5+5smTB1999ZX6ciM9ceVEe/v2bfW4QNHFHnYpOhcXF9StWzfCdmfNmhUXLlywLBGRyKKTA1Kam65cuYIzZ84wbznnzp1TMpATiDTxRD6pvCi2hGDm2HqP8nmIuGXQu1xrtPX5MW8/169fVz14pWev9TwSXnTyuPSwlenffHx8VFlkKLrYw+5EFxoair59+6ptlR5tMlO89GiTOQVlKiZbRBZd8uTJ1SDfXr16qa7hzNvNb7/9pmri1pO51MZfFllOfooARAa2pGGmyHuQWp68L+t7s+bixYtKdtJbVI5RW58f8/bTp08f1cFJTqDW80hk0eXKlQsZMmSAh4eHKosMRRd72J3oQkJCwnq4DRw40FIKNc2Sm5ub5a+IhBfdBx98oCJTRjHvJvL5yxeTIUOGYOTIkernyyL7WXpWbt68Odam8nqbkaZUmT1l0KBBqjem9X3K7+PGjUO7du2QIEECNWTB1ufHvJt88sknYecRSWTR5cuXT007V6xYMTWht+zH8NKj6GIPu2y6lHkMZVvTpUuHWbNmwdfX1/KIbSKLzvo7824jF+tloLf8fFGkJ6VM5SUHsVyLlZ5tZq/VSS1OWhPkvVnfn/X9yuchgrP1eTF6JbLoZF7V8I9ny5YN9+7dU48LFF3sYZeik+Yd60H14Ycfqutz0p1canu2iNx0Kd+6pC1dZrbPnDkz8w4in798UUmbNq36GTnp06cPG4MmkQNX7vdmD6KTaz4y1s763qS2YP0c5Ke8d7kbgq3PjXk3kXOF7JvwX0Iii04mKZBjVmrscm4VyQUHB6vHBYou9rBL0Ql3795F586dw7ZfvgnLtEu2iCw6BwcHdYDKh+Pp6cloGNk3so9Sp06t9pk05UmNTnoy2kuNzno8ytRh0uzO41HfyL6RDmzffPNN2H6LLDq5RidfUh4+fKjKIkPRxR52Kzor0gPzp59+UtteqFAhm7W6yKIrXrz4Cy8YE32QE4x8i5Z9Zs+ikzGAL2qNIPpw6dIldc9D634LLzrpIyDnUjnZynnVFhRd7GF3opOmAPlm9eDBA0sJsGrVKtX8I809ryM6uVgcfn2iJ/LN2Hp82rPo5JY+MrMG0RvpIfwi0d2/f1/1Jpaw1+Xbx+5E5+fnp65lODo6qh5qct1GZqmXbR8xYoRlqYhQdOaEoiM68TLRvQ4UXexhd6KTGtvvv/+u3oh1m2V+wdatW7+wbZyiMycUHdEJik5f7PIanbe3N7Zv365OfDKPoPz+siEGFJ05oeiITlB0+mL3nVFeB4rOnFB0RCcoOn2h6AwoOnNC0RGdoOj0haIzoOjMCUVHdIKi0xeKzoCiMycUHdEJik5fKDoDis6cUHREJyg6faHoDCg6c0LREZ2g6PSFojOg6MwJRUd0gqLTF4rOgKIzJxQd0QmKTl8oOgOKzpxQdEQnKDp9oegMKDpzQtERnaDo9IWiM6DozAlFR3SCotMXis6AojMnFB3RCYpOXyg6A4rOnFB0RCcoOn2h6AwoOnNC0RGdoOj0haIzoOjMCUVHdIKi0xeKzoCiMycUHdEJik5fKDoDis6cUHREJyg6faHoDCg6c0LREZ2g6PSFojOg6MwJRUd0gqLTF4rOgKIzJxQd0QmKTl8oOgOKzpxQdEQnKDp9oegMKDpzQtERnaDo9IWiM6DozAlFR3SCotMXis6AojMnFB3RCYpOXyg6A4rOnFB0RCcoOn2h6AwoOnNC0RGdoOj0haIzoOjMCUVHdIKi0xeKzoCiMycUHdEJik5fKDoDis6cUHREJyg6faHoDCg6c0LREZ2g6PSFojOg6MwJRUd0gqLTF4rOgKIzJxQd0QmKTl8oOgOKzpxQdEQnKDp9oegMKDpzQtERnaDo9IWiM6DozAlFR3SCotMXis6AojMnFB3RCYpOXyg6A4rOnFB0RCcoOn2h6AwoOnNC0RGdoOj0haIzoOjMCUVHdIKi0xeKzoCiMycUHdEJik5fKDoDis6cUHREJ6IrurZt26r1EidOjJUrV1pKSUxA0RlQdOaEoiM6ERXRhYaG4v79++p8ev36dfV7w4YN1XoJEybEmDFjVJmsL497eHhY1iRvAkVnQNGZE4qO6ERURBcYGIipU6eqc03BggXVT+u6H3/8MTJkyKDK8uXLh1q1amHr1q2WNcmbQNEZUHTmhKIjOhHVGt2+ffuQK1cutewHH3wQtl7kVKtWDbdu3bKsSd4Eis6AojMnFB3Riaheo/Pz88Mvv/zyUsl99dVXGDVqlGUN8qZQdAYUnTmh6IhOvElnlB07dqhmSus6kVO5cmVcvHjRsjR5Uyg6A4rOnFB0RCfeRHRSq2vZsmXYOuHz+eefY/To0aqZk0QPis6AojMnFB3RiTcRnbB+/XqkSpUqbD1rSpUqpZ6TRB+KzoCiMycUHdGJNxWd7NtGjRqFrSf58MMPMXToUISEhFiWItGBojOg6MwJRUd04k1FJyxatAgpUqQIW1eGFZw8edLyKIkuFJ0BRWdOXF1dI4hu5syZ6uQgsti7d69pc+bMGfTu3TvseKTozEF0ROfm5oa6deuq9aQXpux/XpuLOSg6g8iik7bxp0+fWh4luiL7KF26dGqfJUqUSM0PKCeW48ePq5qdWePk5ISBAweGHY9VqlSxvGOiMzdu3EDSpEnD9ltURCdMnjxZnYClF6aMsSMxB0VnEFl02bJlU3PN7dy5E5s3b2Y0jOybpUuXhn2Djhs3Ljp06IAJEyZg2LBhGD58uGkzadIk1KtXL+x4lGasLVu2YNu2bTY/C+bdZ9euXZg+fbqavsu636IqOpnqq0aNGmjTpo3qjUliDorOILLoGIZhopuoik6QLzMiTRKzUHQGFB3DMDEduQtBVEQn1+SCgoJUSMxC0Rls2LAhwntkGIaJbr744gtcvXrVcpYh7xKKzkDerPTakw4N8i2MYRgmOpE5KlOnTq06qJB3D0Vn8PjxYxw7dsz0vfUYhtEjcj6RYSIcFqIHFB0hhBC7hqIjhBBi11B0hBBC7Bq7F530etq9e3dYZHooub8T287NjbOzs9qfMsjWyt27d1WZXGt9n6ZPkqnQ5H3LcR0cHGwpJYRYsWvRyczfjRs3jrD9EukN1alTpygP5iT60KVLF7Uv5Q7Ngnxxse7r5s2bv1eiW7ZsmXrftWrVgpeXl6WUEGLFrkUXEBCABg0aqO0uW7asmiJKToIpU6ZUZWXKlFHfhon5+OOPP9Q+tIpuxYoVahqwjBkzqt5u7xNLlixRn0Xt2rXx6NEjSynRGZnia/v27WrKOomccOVkTGIHuxddw4YN1XYvX77cUgrVzJMlSxZVvmDBAkspMROdO3dW+09qdtJ8Kfvz008/xerVqy1LRJ2QJ5dx6u/ZmDFxHEaPGoMxY0Zh1LAxGDt/G3bd84Oujd0y56d8FnXq1KHoTICMrWvSpEmEeTHlxNu3b1/OihJLvDeimzVrlqX0PwYPHqzK5eTA63XmQ0QnN6ds3bo1OnbsqPalSC8wMNCyRFQJhtfRfmhTKj4SZCqAomUqoEKFMihduAzKtxiFSReewNeypG5QdOZBzjWyn2R/Zc2aFePGjcP8+fPVeUpux+Tt7W1ZksQk763oFi5cqO77VKRIER5cJkSkJqJLnjw54sePDwcHB9UZ5c3xxt21P6J8oZwoMekATjrdwA2n67h+9TqcbrvCzS8Yut7rmaIzD+vXr1f7Smpz0rJkRSatuHDhAmt0scR7LTo5UZYoUQI+Pj6WUmIWRHQff/wx0qdPrw5auQ/YkSNHLI++CV64t+YnVCpdErVWu+CNbpLy1BWuTldw5eIlXLr5EA+eBhv1RIMAT7jfe4iHTwIQ4OeGh86XcenSTTi7PbW8ThACH9/C7WtXcNlY76FfCKLSlYaiMw/t27dX+6pChQqWEvI2eG9FN2XKFFVetWpV3mTVhEjTpdTIpelSrm3IvpR7uHl6elqWiCpPcH9tE1QuUwI1VjojykdE0CkcntcMLQplQ46sWZGlans0n3MEZ3194H1xGDo61oRjz9VYuXkAOlUzHs/ogDwtZmL+NU94PtyJzeNroL5DJmQs2gA/LDiEU1H47mXtdUnR6U/16tXVvmratKmlhLwN3hvRyd2nrUhPSxGclA8ZMoS3rDch4TujSJOlNF3K39OmTbMsEVWMGt3qhihXMLdqujxzwxnON+/ijrvfK6RnHDsBV3FoWmU41GuNXxfuwaGzJ3Fs51SMbDYScw8748b5XmiaJz3ifFMPlaeswsYzJ3Fic190rlwEJXMXR6nfOqLTyn9w9Pzf2DS6OopWrIbGG11e+5qg9DiV916zZk14eHhYSomOWM87LVq0sJSQt4Hdi846vKBnz544dOiQuvec3MVXymSYwblz5yxLEzNhHV7Qrl079bfc3fmjjz5C2rRpIwwif30M0W39DY2yJ0KiDHlQoGgRFClaEaWbjceYQ864G/SiL0M+8D0/HO3y50O+wTtx0FoTC32Eh+eccNfzCTxO9UCz/GnwcekhmHjZx3Kt7xyODCuJPBnzoPSUvc9qcJdG4nfHrMjQbguOvmLs9/3793H48GG0bdtWfRZyrMs/NNGXZs2aqX0lYx7J28OuRScXdq09nMJHrs3lypVL3c2XmJNff/1V7UsZFynIdda6deuqsh9++EFNFhA1AvH0/mkc3bAIC+fMwowZ0zB1cj90+8GodZVrhj923YKHracMvY+7mxuiYIqqaLDmJp7vDuOHJ8e64Kd86fC/1quwP6xTqAsuzaqKgmVqoPXecJ2hXObiz2ppkaD8VCx9rOqLL2TEiBFhx7TcYip8qwXRk0WLFqkmd9lfe/futZT+N65OOqO8ea9h8jLsWnSCXKhv06aNupbTqlUrVQOYOnXqG37rJ7qwceNGtV/Dj5s7deqU2r/dunWLoamw/OF7qDc6FE2NNC2WYot78PPiCbyBc7PLIHXyWmi86bZt0R3vgsb5MuLbViuxx9oOGnoDZ6dURoFyNdBmz7PraqHOM9G/UgrEKzkWc11DX9rTc8+ePeqYlmNbrtPxJKk/0rRcvHhxdS6VsZ/Dhw9Xze3yha1y5cqskccSdi86QqJF4H4sbJcJ/8vVA30vPDHqfZHwu4IjY/Pjf0mr48fNt3DPUvyM/0TXJF8GfPvzcuyOLDqp0e16dl3tP9GlRPzS4zHf/eWiI+ZEmpvlemr486rM6iMnXg4viB0oOkJexuN1mNgkFZKUG4HJTk//Gy4QnmAXOK2siVzJHFFntTPuWIqf4Q/vY1Kjo+jIM9zd3bFmzRrVuiTXl3ft2sXxvLEIRUeI8OQC/j22DWud/cPV2m7DeUFz1C5QBEXHH8ZlmxPo+CHg+iR0cciADL8tx0arswJu4OLq3fjX6SHunuqJ5i8QXf5Iogu5MR19KyZH3FITlOjYH5iQ6EPRESK478DqhS3RcMAIjBo7GVMmTcC4yV3Rrmkd1GgyA3OveSPAsuhzBF7B0Rm1Ubl2NdTsNgyjJk3ChMn98UeL8Vh86i5un+6Chpm/xWeNFmG7dcxA6DWcGlcCORzKotnf7pZCo9hlNv6skgQfFx2Bma+4RkcIeT0oOkKEwAd4cHEmZvWph/qFjRqcQ3EUq9UaP87fg79v+r5YcgpDSH6ncWxxWzR3LAwHh2Io2qIfeqy/gOsB/njqNBPDWv2ImiN346S1Vhh6D05ru6HtH70w5mS4W+t478fGEa3wQ6e/sNWLoiMkJqDoCAkjEEG+nvB0c4WrqxvcHj3Bk6j0DQj2hc8jYz1Z97EvfK2WCgmAn6/xmH/Qs2t8oSEICfSD71M/+AeHb6AMRpD/U6Pc2Ba2WxISI1B0hBBC7BqKjhBCiF1D0RFCCLFrKDpCCCF2DUVHCCHErqHoCCGE2DUUHSGEELuGoiOEEGLXUHSEEELsmiiL7u7d5++4RQghhOhMkiRJXl90chdjuTMuwzAMw5ghW7duVXd1f23RMQzDMIyZQ9ExDMMwdh0R3cCBA5+JLlWqVDYXZBiGYRgz5vPPP8egQYOwY8cOxHFyckLKlCmRMGFClQQJEiB+/Pgq8eLFYxiGYRjTJW7cuKpGt2fPHsTx9PTEtm3bsH79eixbtgyzZ8/GhAkTMHLkSAwePFgZUdo5JQMGDGAYhmEYbSOuEsHJT+lYuXPnTsQJCAhASEgIvL291bACGUN3/Phx7N+/H7t27cL27dtVG6fIUHq1MAzDMIyuEV+Jt3bv3q0cJi5TovPx8YGbmxtu3bqFS5cu4cSJEzh06JDqsmldWKwokd8ZhmEYRqeEd5R4S/x1+PBhnDx5Ev8Hgne2ZyxSgQAAAAAASUVORK5CYII=)
In the figure given below, find the area of:
(i) the shaded portion and (ii) the unshaded portion.
![](data:image/png;base64,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)
The shape of the top surface of a table is a trapezium. Find its area if its parallel sides are 1m and 1.2m and perpendicular distance between them is 0.8m .
The shape of the top surface of a table is a trapezium. Find its area if its parallel sides are 1m and 1.2m and perpendicular distance between them is 0.8m .
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)
The figure above is the floor plan drawn by an architect for a small concert hall. The stage has depth 8 meters (m) and two walls each of
length 10 m. If the seating portion of the hall has an area of 180 square meters, what is the value of x ?
Note:
There are different concepts used to solve this problem. Another concept used which is not mentioned in the hint is that the perpendicular drawn from the vertex of an isosceles triangle to the
base cuts the base in half. This property is also applicable in equilateral triangles as they are a special case of isosceles triangle.
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)
The figure above is the floor plan drawn by an architect for a small concert hall. The stage has depth 8 meters (m) and two walls each of
length 10 m. If the seating portion of the hall has an area of 180 square meters, what is the value of x ?
Note:
There are different concepts used to solve this problem. Another concept used which is not mentioned in the hint is that the perpendicular drawn from the vertex of an isosceles triangle to the
base cuts the base in half. This property is also applicable in equilateral triangles as they are a special case of isosceles triangle.