Question

In the figure, ABCD is a square of side 14 cm with centres A, B, C, and D four circles are drawn such that each circle touch externally two of the remaining three circles. Find the area of the shaded region. [3 MARKS]

Answer 1

Concept: 1 Mark
Application: 2 Marks

All the four circles are congruent.

Therefore, unshaded area of the square is equal to one full circle with radius 7 cm.

Area of square
$={14}^2=196c{m}^2$

Area of circle
$=\pi (7{)}^2=153.86c{m}^2$

Area of shaded portion
$=196-153.86$

$=42.14c{m}^2$