A, B, C, D are the mid points of sides PQ, QR, RS and SP respectively of parallelogram PQRS. If area of the parallelogram shaped region PQRS = 36 sq.cm then area of the region ABCD is

Given

A, B, C, D are the mid points of sides PQ, QR, RS and SP respectively of parallelogram PQRS. If area of the parallelogram shaped region PQRS = 36 sq.cm

Formula used.

If one triangle and one parallelogram are on same base and both are between 2 parallel lines then Area of triangle gets half of parallelogram

Solution

Join BD

Parallelogram BDPQ and triangle ADB are on same base BD

And PQ || BD

Thus;

Area of triangle ABD = × Area of parallelogram BDPQ

Parallelogram BDSR and triangle CDB are on same base BD

And SR || BD

Thus;

Area of triangle CBD = × Area of parallelogram BDSR

Adding both we get

Area of[Δ ABD+Δ CBD]= × Area of parallelogram [BDPQ+BDSR]

Area of ABCD parallelogram = × Area of PQSR parallelogram

Area of ABCD parallelogram = × 36 cm² = 18 cm²