Notes
rectangles stacked in a semi-circle solution

Rectangles Stacked in a Semi-Circle

Solution by Pythagoras' Theorem

With the points labelled as above, let $a$ be the length of $A B$ and $b$ the length of $C D$. As the rectangles are identical, $O A$ has length $2 b$. The radius of the circle is $5$, so $O B$ has length $5$. Applying Pythagoras' theorem to triangle $O A B$ shows that:

Then $O C$ also has length $5$ and $O D$ has length $2 a$, so applying Pythagoras' theorem to triangle $O D C$ shows that:

Subtracting these equations shows that $3 b^2 = 3 a^2$. Since both $a$ and $b$ are lengths, and so positive, this means that $a = b$, and $a^2 = 5$. The area of a single rectangle is $2 b \times a = 2 a^2$, so the area of all three is $6 a^2 = 6 \times 5 = 30$.