CIRCUMERENCES AND PERIMETERS

COMPOSITE

Concept: Perimeter is a measure of the distance around the edge of any flat shape. To find the perimeter of a polygon, add the lengths of its sides. The perimeter of a circle is called the circumference. The formula used to find the circumference of a circle is:. Note: The Pythagorean Theorem is often necessary to solve these problems (a2 + b2 = c2). Some figures may be made up of several shapes. To find the perimeter of a combined figure, find the perimeter of each of the parts and add the results. Some problems may require multiple steps, and/or variations on the Steps listed below.

Steps for Finding the Perimeter and Circumference

Step 1 | Divide the figure into simple shapes. For each shape work Steps 2, 3, and 4.
Step 2 | Choose the proper formula for the first shape in the problem.
Step 3 | Substitute the values.
Step 4 | Solve.
Step 5 | Repeat Steps 2, 3, and 4 as needed.
Step 6 | Combine perimeters.
Step 7 | Write the final answer.

Example Solve the perimeter of the shaded area, given S = 3

| There are two shaded triangles. Each shaded triangle has two equal sides. We can use the Pythagorean theory to determine the third side of each triangle. We can then add all sides together to find our answer. |
Step 1 | Divide the figure into simple shapes. |
Step 2 | Choose the proper formula for the first shape in the problem. | A2 + B2 = C2
Step 3 | Substitute the values. | 32 + 32 = C2
Step 4 | Solve. | 32 + 32 = C2 9 + 9 = C2 18 = C2 4.25 = C
| We now have the missing measurement for both shaded triangles. Return to Step 1 with a new formula and the additional value just found. |
Step 5 (Step 2) | Repeat Steps 2, 3, and 4 as needed. Choose the proper formula for the first shape in the problem. | S1 + S2 + S3 = P
Step 5 (Step 3) | Substitute the values. | 3 + 3 + 4.25 = P
Step 5 (Step 4) | Solve | 3 + 3 + 4.25 = 10.25
Step 5 (Step 2) | Repeat Steps 2, 3, and 4 as needed. Choose the proper formula for the second shape in the problem. | S1 + S2 + S3 = P
Step 5 (Step 3) | Substitute the values. | 3 + 3 + 4.25 = P
Step 5 (Step 4) | Solve | 3 + 3 + 4.25 = 10.25
Step 6 | Combine perimeters. | 10.25 + 10.25 = 20.5
Step 7 | Write final answer. | P = 20.5