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O is any point on the diagonal PR of a parallelogram PQRS. Prove that the areas of triangle PSO and PQO are equal.

One diagonal of a rhombus is twice as long as the other diagonal. If the rhombus has area 128 cm\(^2\), find the length of the shorter diagonal.

The sides of a triangular plot are in the ratio 3 : 5 : 7; its perimeter is 300m. Find its area.

Find the area of a triangle, given that its sides are 8 cm and 11 cm long, and its perimeter is 32 cm.

The parallel sides of a trapezium are 40 cm and 20 cm. If its non-parallel sides are both equal, each being 26 cm, find the area of the trapezium.

Find the area of triangle ADE in the given figure.

The ratio of the perimeters of two circles is 5:4. What is the ratio of their radii?

Find the total perimeter of all the petals of the given flowers.

If the diameter of a car tyre is 56 cm, then:
(i) How far does the car need to travel for the car to complete one revolution?
(ii) How many revolutions does the tyre make if the car travels 10 km?

Find the perimeters of the following shapes(taking the arcs to be quarter or half or three-quarters of a circle, as appropriate):