Geometry
# Composite Figures

As 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 \(A + B + C + D + E\).

×

Problem Loading...

Note Loading...

Set Loading...