## Trisect Diameter There are several ways to trisect a circular region, but this is one of the prettiest. Trisect the diameter, and then draw semicircles on it as shown. Your job is to prove that the three wavy regions have the same area.

(You may assume that the area of I equals the are of III.)

## Square and Triangles Area In this diagram, not drawn to scale, figures I and III are equilateral triangular regions with areas of 32√3 and 8√3 square inches, respectively. Figure II is a square region with area 32 square inches. Let the length of segment AD be decreased by 12.5% of itself, while the lengths of AB and CD remain unchanged. What’s the percent decrease in the area of the square?

1. 12.5
2. 25
3. 50
4. 75
5. 87.5

## Parallelogram, Triangle Areas In parallelogram ABCD, M and N are midpoints of sides AD and BC, respectively. DN intersects AB at P, CM intersects AB at Q, and DN intersects CM at O. If the area of parallelogram ABCD is 24 square cm, find the area of triangle QPO.

## Area Sum of Equilateral Triangles 1 Here are two equilateral triangles; one has side x and the other y. Find the length of the side of an equilateral triangle whose area is the sum of the areas of these two triangles.