# Two Circles, Two Squares +-- {.image} [[TwoCirclesTwoSquares.png:pic]] > Two circles, two squares. What's the shaded area? =-- ## Solution by [[square|Properties of Squares]] +-- {.image} [[TwoCirclesTwoSquaresLabelled.png:pic]] =-- In the above diagram, the height of the square is the side length of the shaded square plus the length of $A C$ and is also the combined lengths of $A B$, $F G$, and $G H$. Since both $A B$ and $G H$ are radii of the circles, this means that the height of the shaded square is the same as the length of $F G$. The shaded square is therefore congruent to $B F G D$. Since the [[square|area of a square]] is half the square of its diagonal, and the diagonal of $B F G D$ is two radii of the circles, the area is $\frac{1}{2} \times 8^2 = 32$.