Find the area of the figure.
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The system of equations above is graphed in the xy -plane. At which of the following points do the graphs of the equations intersect?

Note:
We can solve the equations by other methods too, but the method of substitution is most suitable here. Also, instead of solving
 by middle term factorisation, we could also use the quadratic formula, which is given by

Where the standard form of equation is 

Find the area of an isosceles trapezium ABCD, if the parallel sides are 6cm and 14 cm, its non parallel sides is 5cm each.

 and  Solve by using the elimination method.

The sides of a parallelogram are 12cm and 8cm. one of the diagonal is 10cm long. If d is the length of the other diagonal, then which of the following is correct?

Cylindrical vessel of diameter 9 cm has some water in it. A cylindrical iron piece of diameter 6 cm and height 4.5 cm is dropped in it. After it was completely immersed, find the rise in the level of water.

During mineral formation, the same chemical compound can be come different minerals depending on the temperature and pressure at the time of formation. A phase diagram is a graph that shows the conditions that are needed to form each mineral. The graph above is a portion of the phase diagram for aluminosilicates, with the temperature t , in degrees
Celsius  , on the horizontal axis, and the pressure p , in gigapascals (G Pa), on the
Which of the following systems of inequalities best describes the region where sillimanite can form?

Note:
We do not have the exact inequalities in the option, so we choose the one from the options which is the closest approximation of the inequalities that we have calculated. There are a couple of formulas and concepts used here, such as the equation of a line passing through two points and the concept that the region below a line is given by replacing the equality sign with less than or equal to in the standard form of the equation and vice versa.

If two angles and the included side of one triangle are congruent to two angles and the included side of a second triangle, then the two triangles are congruent by

Solve:  and  by using elimination method.

ABCD is a parallelogram of area 162 sq., P is the point on AB such that AP:PB = 1:2, calculate the area of Triangle APD and the ratio PQ:QD, where Q is the point of intersection of AC and PD

How many litres of water flows out through a pipe having an area of cross-section of 5 cm² in one minute, if the speed of water in pipe is 30 cm/sec?

Curved surface area of a right circular cylinder of height 14 cm is 88 cm². Find the volume of the cylinder.

The sides of a parallelogram are 3cm and 2cm and the distance between two longer sides is 1.5cm. Find the distance between the shorter sides?

Solve:  and 

The cross section of a canal is atrapezium in shape. If the canal is 10m wide at the top and 6m wide at the bottom and the area of the cross section is 840 sq. m, find the depth of the canal ?

The total surface area of a cylinder of height 6.5 cm is 220 sq. cm. Find its volume.