Semicircle Stack
Age
14 to 16
Challenge level
What is the total area enclosed by the three semicicles?
Problem
Image
The diagram shows three semicircles, each of radius one.
What is the size of the total area shaded?
Student Solutions
Image
The shaded area may be divided into a $ 2 \times 1$ rectangle plus a semicircle plus two quarter circles
(all of radius $1$).
Hence the total area is that of the rectangle
plus a circle of radius $1$ which equals $2 + \pi$