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 ΔOPB.

Answer 1

Area of ΔOPB = 8 cm²

Step-by-step explanation:

Given data:

ABCD is a square.

P is the midpoint of AB and Q is the midpoint of CD.

PQ and BD intersect at O.

AB = 8 cm

Since P is the midpoint of AB,

$B P=\frac{1}{2}A B$

     $=\frac{1}{2}\times8$

BP = 4 cm

APQD is a rectangle.

$P O=\frac{1}{2} A D$

Area of triangle = $\frac{1}{2} \times\text{base}\times\text{height}$

Area of ΔOPB =  $\frac{1}{2} \times \mathrm{BP} \times \mathrm{PO}$ (using(1))

                        $=\frac{1}{2} \times 4 \times 4$

                        $=\frac{1}{2} \times 16$

                        = 8 cm²

Area of ΔOPB = 8 cm²

Hence, area of ΔOPB = 8 cm².

To learn more...

1. The area of a square ABCD is 64 square centimetre. find the area of square obtained by joining the midpoint of the side of the square ABCD.

https://brainly.in/question/1897646

2. Find the area of the triangle formed by joining the midpoint of the sides of triangle whose vertices A(2,3)B(4,-4)C(2,6).

https://brainly.in/question/12559902