Semicircle Shape
Find the shaded area of these shapes with perimeters made of semicircles.
Age
11 to 14
Challenge level
Problem
Image
The figure shows two shapes that fit together exactly.
The outline of each shape is formed by four semicircles of radius 1.
What is the total shaded area?
Student Solutions
Drawing on two squares, which will each have side length 2 (equal to the diameter of the semicircles), gives this diagram:
Image
A total of 3 semicircles have been cut out of the squares, and there are 3 semicircles sticking out of the squares.
So the shaded area is equal to the area of the two squares, which is 2$\times$2 + 2$\times$2 = 8.