Maths-
General
Easy
Question
An isosceles triangle has perimeter 30 cm and each of the equal sides is 12 cm. Find the area of triangle.
Hint:
Use the formula ,
The correct answer is: 34.86 cm2
Let length of the third side = b
It is given that perimeter of triangle = 30 cm
12 + 12 + x = 30
x = 30 – 24 = 6 cm
Area of an isosceles triangle =
where a is length of equal side and b is third side
So, a = 12 and b = 6 cm
Area of an isosceles triangle = ![6 over 2 square root of 12 squared minus 6 squared over 4 end root equals 3 square root of 144 minus 36 over 4 end root](data:image/png;base64,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)
= ![3 square root of 135 equals 9 square root of 15](data:image/png;base64,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)
= 34.86 cm2
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