Question

2 squares are shown. The first square has a circle cut out of the middle. The second square has 2 halves of the same size circle cut out of the middle.
Isla says the areas of the two shaded regions are equal. Clara says the shaded region in the first figure has a larger area. Who is correct?

Isla is correct because each figure subtracts an equal area from the area of the square.
Isla is correct because it is the sum of the area of the circle and the area of the square.
Clara is correct because the area of the circle is less than that of the two semicircles.
Clara is correct because the area of the two semicircles is less than that of the circle.

Answer 1

Isla is correct. The full circle removed in the first square has the same area as the two semicircles combined in the second square, so each square loses the same area from the square. Therefore the shaded regions are equal.