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Name
Class
Date
Practice
Form K
10-5 Trigonometry and Area
Find the area of each regular polygon. Round your answers to the nearest tenth.
1. pentagon with side length 8 in.
To start, find the measure of a central angle.
Then use trigonometry to find a.
The measure of the central angle of the regular
1
360
pentagon is
=
so, mC  ·
=
2
5
4
4
4
=
= ?
tan 36° = ; a =
a
tan 36
?
.
2. hexagon with side length 9 m
3. decagon with radius 4 mm
4. octagon with radius 10 cm
5. 20-gon with radius 5 in.
6. 15-gon with perimeter 90 ft
7. 18-gon with perimeter 126 m
Find the area of each triangle. Round your answers to the nearest tenth.
8.
To start, write the SAS formula, then substitute
given values into the formula.
1
A  bc (sin A)
2

1
2
(sin 92°)
9.
10.
11.
12.
Prentice Hall Foundations Geometry • Teaching Resources
Copyright © by Pearson Education, Inc., or its affiliates. All Rights Reserved.
45
Name
Class
Date
Practice (continued)
Form K
10-5 Trigonometry and Area
13. ABCDEFGH is a regular octagon with center X and radius 5 cm.
Find each measure to the nearest tenth.
a. mFXE
b. mYXE
c. XY
d. FE
e. perimeter of ABCDEFGH
f. area of ABCDEFGH
Find the perimeter and area of each regular polygon to the nearest tenth.
14.
15.
16.
17. The Rileys are replacing the carpet on their outdoor deck. The deck is a regular
hexagon with radius 9 ft. The cost for carpet and installation is $3.75/ft2. What
will it cost to replace the carpet?
The polygons are regular polygons. Find the area of the shaded region to the
nearest tenth.
18.
19.
20.
21. Which has the greater area, a regular octagon with side length 10 ft, or a
regular nonagon with side length 10 ft? Justify your answer.
22. Several streets intersect to form triangles near Dupont Circle in
Washington, D.C. One such triangle is formed by New Hampshire
Avenue, Massachusetts Avenue, and 16th Street. The section of New
Hampshire Avenue is about 3100 ft long. The section of 16th Street is
about 3500 ft long. The angle enclosed by the two streets has a measure
of about 35. What is the area of this triangle, to the nearest 100 ft2?
Prentice Hall Foundations Geometry • Teaching Resources
Copyright © by Pearson Education, Inc., or its affiliates. All Rights Reserved.
46
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