Find Perimeter, Circumference, & Area 1.7 Find Perimeter, Circumference, & Area

Objectives Find dimensions of polygons.

Perimeter The perimeter of a polygon is the distance around the figure or the sum of all of the lengths of its sides. In a circle, the perimeter is referred to as the circumference. Perimeter and circumference are measured in unit lengths, such as meters (m) and feet (ft).

Area The area of a polygon or a circle is the amount of surface covered by a figure. Area is measured in square units of length, such as square meters (m2) and square feet (ft2).

Formulas

Example 1a: CONSTRUCTION A masonry company is contracted to lay three layers of decorative brick along the foundation for a new house given the dimensions below. Find the perimeter of the foundation and determine how many bricks the company will need to complete the job. Assume that one brick is 8 inches long.

Example 1a: First, find the perimeter. Add the lengths of the sides. The perimeter of the foundation is 216 feet.

Example 1a: Next, determine how many bricks will be needed to complete the job. Each brick measures 8 inches, or foot. Divide 216 by to find the number of bricks needed for one layer. Answer: The builder will need 324 bricks for each layer. Three layers of bricks are needed, so the builder needs 324 • 3 or 972 bricks.

Example 1b: CONSTRUCTION The builder realizes he accidentally halved the size of the foundation in part a. How will this affect the perimeter of the house and the number of bricks the masonry company needs?

Example 1b: The new dimensions are twice the measures of the original lengths. The perimeter has doubled. The new number of bricks needed for one layer is or 648. For three layers, the total number of bricks is 648 • 3 or 1944 bricks. Answer: The perimeter and the number of bricks needed are doubled.

Your Turn: SEWING Miranda is making a very unusual quilt. It is in the shape of a hexagon as shown below. She wants to trim the edge with a special blanket binding. The binding is sold by the yard. a. Find the perimeter of the quilt in inches. Then determine how many yards of binding Miranda will need for the quilt. Answer: 336 in., yd

Your Turn: SEWING Miranda is making a very unusual quilt. It is in the shape of a hexagon as shown below. She wants to trim the edge with a special blanket binding. The binding is sold by the yard. b. Miranda decides to make four quilts. How will this affect the amount of binding she will need? How much binding will she need for this project? Answer: The amount of binding is multiplied by 4. She will need yards.

Example 2: Find the perimeter of pentagon ABCDE with A(0, 4), B(4, 0), C(3, –4), D(–3, –4), and E(–3, 1).

Example 2: Use the Distance Formula, , to find AB, BC, CD, DE, and EA.

Example 2: Answer: The perimeter of pentagon ABCDE is or about 25 units.

Your Turn: Find the perimeter of quadrilateral WXYZ with W(2, 4), X(–3, 3), Y(–1, 0), and Z(3, –1). Answer: about 17.9 units

Example 3: The width of a rectangle is 5 less than twice its length. The perimeter is 80 centimeters. Find the length of each side. Let represent the length. Then the width is .

Example 3: Perimeter formula for rectangle Multiply. Simplify. Add 10 to each side. Divide each side by 6. The length is 15 cm. By substituting 15 for , the width becomes 2(15) – 5 or 25 cm. Answer:

Your Turn: The length of a rectangle is 7 more than five times its width. The perimeter is 134 feet. Find the length of each side. Answer:

Assignment Pre- AP Geometry Pgs. 52 – 54 #4 – 18, 28, 30, 32