Solution of the Week #501 - Rectangle and Quarter Circle

The first thing we can do is to work out the radius of the quarter circle. We can form a right triangle on the figure that has hypotenuse r and legs 6 and (r-2).

Using Pythagoras this works out as r=10.

If we make a copy of the figure, rotate it 90 degrees and place it next to the original figure we can see what the length and width of the rectangle are in terms of the radius.

Since we already know r=10, we find that the rectangle measures 14 x 4 units.