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Example 6-1a Name the polygon by its number of sides. Then classify it as convex or concave, regular or irregular. There are 4 sides, so this is a quadrilateral. No line containing any of the sides will pass through the interior of the quadrilateral, so it is convex. The sides are not congruent, so it is irregular. Answer: quadrilateral, convex, irregular

Example 6-1b Name the polygon by its number of sides. Then classify it as convex or concave, regular or irregular. There are 9 sides, so this is a nonagon. A line containing some of the sides will pass through the interior of the nonagon, so it is concave. The sides are not congruent, so it is irregular. Answer: nonagon, concave, irregular

Example 6-1c Answer: triangle, convex, regular Answer: quadrilateral, convex, irregular Name each polygon by the number of sides. Then classify it as convex or concave, regular or irregular. a. b.

Example 6-2a 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 6-2b First, find the perimeter. Add the lengths of the sides. The perimeter of the foundation is 216 feet.

Example 6-2c 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 or 972 bricks.

Example 6-3a Find the perimeter of pentagon ABCDE with A(0, 4), B(4, 0), C(3, –4), D(–3, –4), and E(–3, 1).

Example 6-3b Use the Distance Formula,, to find AB, BC, CD, DE, and EA.

Example 6-3c Answer: The perimeter of pentagon ABCDE is or about 25 units.

Example 6-3d 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 6-4a 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 6-4b Perimeter formula for rectangle Multiply. Simplify. Add 10 to each side. Divide each side by 6. Answer: The length is 15 cm. By substituting 15 for, the width becomes 2(15) – 5 or 25 cm.

Example 6-4c 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: