In square AB2CD, P and Q are mid-point of AB and CD respectively. If AB = 8 cm and PQ and BD intersect at O, then find area of ΔOPB.

Question

In square AB2CD, P and Q are mid-point of AB and CD respectively. If AB = 8 cm and PQ and BD intersect at O, then find area of &#x394;OPB.

Philoid · Accepted Answer

Given: ABCD is a square

P and Q are the mid points of AB and CD respectively.

AB = 8cm

PQ and BD intersect at O

Now,

AP = BP = AB

AP = BP = * 8

= 4 cm

AB = AD = 8 cm

QP ‖ AD

Then,

AD = QP

So,

OP = AD

OP = * 8

= 4 cm

Now,

Area ( = * BP * PO

= * 4 * 4

= 8 cm²

Hence, Area ( is 8 cm²