Geometry
# Composite Figures

$\color{#BA33D6}{Violet}$ region (four square looking region of central circle) if radius of each circle is 4 units.

Find the area ofAs shown, a rectangle (*not* a square) is partitioned into four triangles: 1 equilateral and 3 right triangles. The areas of two of the right triangles are 30 and 50. Find the area $x$ of the remaining right triangle.

**Bonus:** Find the general relationship among the areas of the 3 right triangles.

Suppose we combine a unit circle and a square of the same area, as shown above, such that their centroids lie on the same point. What is the area of the non-overlapping white region?

If your answer is of the following form $A \arctan\left(\dfrac{\sqrt{\pi\left(B - \pi\right)}}{\pi - C}\right) - D \sqrt{\pi\left(E - \pi\right)},$ where $A, B, C, D,$ and $E$ are positive integers, evaluate $A + B + C + D + E$.