Assignment 4

1. Find the area of the shaded region where the petals are formed by constructing semicircles. For each semicircle, the center is the midpoint of the side.

2. A farmer has a square field that measures 100 m on a side. He has a choice of using one large circular irrigation system or four smaller ones, as illustrated.

a. What percent of the field will the larger system irrigate?b. What percent of the field will the smaller system irrigate?c. Which system will irrigate more land?d. What generalizations does your solution suggest?

3. The following figure shows five concentric circles. If the width of each of the rings formed is the same, how do the areas of the two shaded regions compare?

4. Find the area of each of the following shaded parts. Assume all arcs are circular.

5. A stop sign is to be made by cutting off triangles from the corners of a square sheet of metal 32 inches on a side. What length x will leave a regular octagon?

6. ABCD is a parallelogram. AD = 15 cm, DE = 10 cm and DF = 12 cm. Find

a. the area of the parallelogramb. the perimeter of the parallelogram

7. In the figure, ABEG is a rectangle and E and G are the centers of the circles. If BE = 7 cm and the areas of the shaded part ABC and the shaded part CDF are equal, find GE.

8. In the figure, AC is an arc of a circle with center O. BDA is a semicircle with center M. If OA is perpendicular to BA and OA = BA = 14 cm, find the total area of the shaded parts.

9. OAB is a quadrant of radius 7 cm. Find the total area of the shaded parts.

10. Use Pick's formula to find the approximate areas of these irregular shapes.