Question

In the two pictures below, the squares are of the same size.

Prove that the green regions are of the same area.

Answer 1

Let ‘a’ be the side of the square in the picture.

Area of the square = a²

i. If the four sectors in the vertices are joined together, a circle is formed because the radius of each sector is a/2.

Area of the shaded part = Area of the square – area of the circle.

ii. In the second picture diameter of the circle = a Radius = a/2

Area of the shaded part = Area of the square – area of the circle.

i.e., Areas of the shaded portions are equal.