# In Square Abcd, P and Q Are Mid-point of Ab and Cd Respectively. If Ab = 8cm and Pq and Bd Intersect at O, Then Find Area of δOpb. - Mathematics

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

#### Solution

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 ΔOBP8 cm2

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#### APPEARS IN

RD Sharma Mathematics for Class 9
Chapter 14 Areas of Parallelograms and Triangles
Q 6 | Page 60