We know that when a parallelogram and a triangle are on the same base and between the same parallels then area of a triangle is half the area of parallelogram. Area of triangle = 1/2 area of parallelogram Area of triangle / Area of parallelogram = 1/2

In the given figure, ar(△ECD) = 1/2 x ar(൏ ABCD) ∵ If a triangle and a parallelogram are on the same base and between the same parallels, the area of the triangle is equal to one-half area of the parallelogram.

If a parallelogram and a triangle are on the same base and between the same parallels then the area of the triangle is half the area of parallelogram. But here the base of the triangle ABC is neither the same nor equal to the base of the parallelogram PQRS. Therefore, ar(△ABC) ≠ 1/2 ar(PQRS)

ABCD and BECD are parallelograms. ar(ABCD) = ar(BECD) = 36cm² If a parallelogram and a triangle are on the same base and between the same parallels then the area of the triangle is half the area of parallelogram. ar(△BCD) = 1/2 ar(ABCD) ar(△BCD) = 1/2 × 36 ar(△BCD) = 18 cm²

Since PR is a diagonal of the parallelogram PQRS and diagonal of a parallelogram divides the parallelogram in two triangles of equal area, therefore, ar (△PRQ) = ar(△PSR) .........(1) ar (△PSR) = ar (△PSA) + ar (△PAR) ar (△PSR) = 15 + 30 = 45 cm² .........(2) From (1) and (2), ar (△PRQ) = 45 cm²