# Five Circles in a Rectangle in a Semi-Circle +-- {.image} [[FiveCirclesinaRectangleinaSemiCircle.png:pic]] > Each of the small circles has area $1$. What’s the area of the semicircle? =-- ## Solution by [[Pythagoras' Theorem]] and [[Circle Area]] +-- {.image} [[FiveCirclesinaRectangleinaSemiCircleLabelled.png:pic]] =-- Let $r$ be the radius of the smaller circles, so $\pi r^2 = 1$, and let $R$ be the radius of the semi-circle. Then with the points labelled as in the diagram above, the length of $A B$ is $2 r$, of $O A$ is $5 r$, and of $O B$ is $R$. Applying [[Pythagoras' theorem]] to triangle $O A B$ shows that: $$ R^2 = (2 r)^2 + (5 r)^2 = 29 r^2 $$ The area of the semi-circle is therefore: $$ \frac{1}{2} \pi R^2 = \frac{29}{2} \pi r^2 = \frac{29}{2} $$