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]

Open in App

Solution

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
$= 14^{2} = 196 c m^{2}$

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

Area of shaded portion
$= 196 - 153.86$

$= 42.14 c m^{2}$

Suggest Corrections

Similar questions

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]

In the given figure, ABCD is a square of side 14 cm. With centres A, B, C and D, four circles are drawn such that each circle touches externally two of the remaining three circles. Find the area of the shaded region.

In Fig. 12.25, ABCD is a square of side 14 cm. With centers A, B, C and D, four circles are drawn such that each circle touches externally two of the remaining three circles. Find the area of the shaded region.