What is the area in square units of the entire colored region?

Question

Consider that the area of the square is 16 square units and the area of the circle is 20 square units, but suppose you know that the area of the region defined by the intersection of the square and the circle measures 7 square units.

What is the area in square units of the entire colored region?

Answer 1

If the area of the square is 16 sq units and the area of the intersection is 7 sq units then the area of the square outside the circle is 16 - 7 = 9 square units. So the area of the total combined figure is the area of the circle (20 sq units) + 9 square units = 29 sq units.

Answer 2

Area of the circle =16 square units

area of the circle =20 square units

area at the intersection = 7 square units

are of the red region of the square = 16-7= 9 square units

total area of the the colored region= area of the circle + area of the red region = 20+9=29 square units