# Semi-Circle Splitting a Triangle +-- {.image} [[SemiCircleSplittingaTriangle.png:pic]] > The equilateral triangle has been split into two equal areas. What’s the area of the semicircle? =-- ## Solution by [[Area Scale Factor]] and [[equilateral|Lengths in Equilateral Triangles]] +-- {.image} [[SemiCircleSplittingaTriangleLabelled.png:pic]] =-- With the points labelled as above, the orange triangle has half the area of the full triangle, so the length of $E F$ is $\frac{1}{\sqrt{2}}$ of the length of $A B$, so is $4\sqrt{2}$. The height $O C$ is then $\frac{\sqrt{3}}{2}$ times the length of $E F$, so is $\frac{\sqrt{3}}{2} \times 4 \sqrt{2} = 2\sqrt{6}$. The area of the semi-circle is therefore $\frac{1}{2} \pi (2 \sqrt{6})^2 = 12 \pi$.