Question

Four circles or diameter d cm are arranged in such a way that they touch each other (as shown below). A square is formed by joining the centres of the four circles.

What is the area of the shaded part?

A) d2(1-π)
B) d2(4-π)
C) d2/4-πd2/4
D) d2-πd2/4

Answer 1

D. d^2 - πd^2/4.

Explanation:

The sides of the square are equal to the diameter of the circles so the area of the square = d^2.

The shaded area = area of the square - 4 * the area of a quarter circle

= area of the square - area of 1 circle

= d^2 - π r^2

r = d/2 so

Area of the shaded part = d^2 - π (d/2)^2

= d^2 - π (d^2/4)