Question

A, B, C, D are mid-points of sides of parallelogram PQRS. If ar (PQRS) = 36 cm², then ar (ABCD) =

(a) 24 cm²

(b) 18cm²

(c) 30 cm²

(d) 36 cm²

Answer 1

Given:

(1) PQRS is a parallelogram.

(2) A, B, C, D are the midpoints of the adjacent sides of Parallelogram PQRS.

(3)

To find:

Calculation:

A and C are the midpoints of PS and QR respectively.

Now PQRS is a parallelogram which means

AP = CQ ……..(1)

Also, PS || QR

AP || CQ ……(2)

From 1 and 2 we get that APCQ is a parallelogram.

Since Parallelogram APCQ and ΔABC are on the base AC and between the same parallels AC and PQ.

……(3)

Similarly ,

……(4)

Adding 3 and 4 we get,

Hence the correct answer is option (b).