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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

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

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.

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.

First, find the perimeter.

Add the lengths of the sides.

The perimeter of the foundation is 216 feet.

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.

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

Use the Distance Formula, ,

to find AB, BC, CD, DE, and EA.

Answer: The perimeter of pentagon ABCDE is

or about 25 units.

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

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 .

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.

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: