Question

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

Answer 1

Given: Here from the given question we get

(1) ABCD is a square,

(2) P is the midpoint of AB

(3) Q is the midpoint of CD

(4) PQ and BD intersect at O.

(5) AB = 8cm

To find : Area of ΔOPB

Calculation: Since P is the midpoint of AB,

`BP = 1/2 (AB) `

      = 1/2 (8)`

     = 4 cm 

BP = 4cm ……(1)

Area of triangle = `1/2 `× base × height 

Area of ΔOPB = `1/2` × BP × PO (from 1)

                        ` = 1/2 × 4 × (PO = 1/2 AD , APQD ` is a rectangle)

                       `= 1/2 × 16 `

Area of ΔOPB = 8 cm²

Hence we get the Area of ΔOBP =  8 cm²