In square ABCD, P and Q are mid-point of AB and CD respectively. If A

1.	In square ABCD, 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.
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 = \(\frac{1}{2}\) AB AP = BP = \(\frac{1}{2}\) x 8 = 4 cm AB = AD = 8 cm QP ‖ AD Then, AD = QP So, OP = AD OP = \(\frac{1}{2}\) x 8 = 4 cm Now, Area (ΔOPB) = \(\frac{1}{2}\) x BP x PO = \(\frac{1}{2}\) x 4 x 4 = 8 cm² Hence, Area (ΔOPB) is 8 cm²

In square ABCD, 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.

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 = \(\frac{1}{2}\) AB

AP = BP = \(\frac{1}{2}\) x 8

= 4 cm

AB = AD = 8 cm

QP ‖ AD

Then,

AD = QP

So,

OP = AD

OP = \(\frac{1}{2}\) x 8

= 4 cm

Now,

Area (ΔOPB) = \(\frac{1}{2}\) x BP x PO

= \(\frac{1}{2}\) x 4 x 4

= 8 cm²

Hence,

Area (ΔOPB) is 8 cm²