Question

Rectangle ABCD has AB = 4 and BC= 8. Construct arc AE centered at B with E on side BC and construct arc CF centered at E with F along side AD. What is the area of AFCE, the region shaded in blue?

in blue?

Answer 1

Answer: 16

Explanation:

Note that if you move the shaded area in square
`FABE` to square
`DFEC`, the shaded area is exactly half that of the entire rectangle.

The area of the entire rectangle is
`4(8)=32`, so the area of the shaded region is 16.