Question

In the given figure, two circle with centres A and B touch each other at the point T. If AT = 14 cm and AB = 3.5 cm, find the area of the shaded region.

• A. $269.5c{m}^2$
• B. $270.5c{m}^2$
• C. $271.5c{m}^2$
• D. $272.5c{m}^2$

Answer 1

The correct option is A $269.5c{m}^2$

Radius of the circle with center at A $=AT=14cm$
Radius of the circle with center at B $=AT-AB=(14-3.5)cm=10.5cm$
Area of the circle with center A $=\pi (14{)}^2$
$=616c{m}^2$
Area of the circle with center B $=\pi (10.5{)}^2$
$=346.5c{m}^2$
Thus, area of the shaded region $=(616-346.5)c{m}^2$
$=269.5c{m}^2$