Question

In Fig, a square OABC is inscribed in a quadrant OPBQ. If OA = 20 cm, find the area of the shaded region. $(Use\pi =3.14)$

• A. $228c{m}^2$
• B. $128c{m}^2$
• C. $236c{m}^2$
• D. $298c{m}^2$

Answer 1

The correct option is A

$228c{m}^2$

Side of square = OA = AB = 20 cm
Radius of the quadrant = OB
OAB is right angled triangle
By Pythagoras theorem in $\Delta OAB$ ,
$O{B}^2=A{B}^2+O{A}^2\Rightarrow O{B}^2={20}^2+{20}^2\Rightarrow O{B}^2=400+400\Rightarrow O{B}^2=800\Rightarrow OB=20\sqrt{2}cm$
Area of the quadrant
$=\frac{\left(\pi R^2\right)}{4}c{m}^2$
$=\frac{3.14}{4}\times (20\sqrt{2}{)}^{2}c{m}^2=628c{m}^2$
Area of the square
$=20\times 20=400c{m}^2$
Area of the shaded region
= Area of the quadrant - Area of the square
$=(628-400)c{m}^2=228c{m}^2$