NAME ______________________________________________ DATE
1-6
____________ PERIOD _____
Study Guide and Intervention
(continued)
Polygons
Perimeter The perimeter of a polygon is the sum of the lengths of all the sides of the
polygon. There are special formulas for the perimeter of a square or a rectangle.
Example
Write an expression or formula for the perimeter of each polygon.
Find the perimeter.
a.
b.
4 in.
b
5 cm s
c
3 in. a
5 in.
c.
5 cm
s
3 ft
,
s 5 cm
2 ft w
s
5 cm
P5a1b1c
531415
5 12 in.
w
,
P 5 2, 1 2w
5 2(3) 1 2(2)
5 10 ft
P 5 4s
5 4(5)
5 20 cm
Exercises
Find the perimeter of each figure.
1.
2.
3 cm
2.5 cm
5.5 ft
square
3.5 cm
3.
4.
27 yd
19 yd
1 cm
14 yd
12 yd
24 yd
Find the length of each side of the polygon for the given perimeter.
5. P 5 96
6. P 5 48
x
2x
rectangle
©
x
x22
x
Glencoe/McGraw-Hill
2x
32
Glencoe Geometry
NAME ______________________________________________ DATE
1-6
____________ PERIOD _____
Skills Practice
Name each polygon by its number of sides and then classify it as convex or
concave and regular or irregular.
1.
2.
3.
4.
5.
6.
Find the perimeter of each figure.
7.
8.
20 yd
9.
6m
4m
20 yd
18 yd
40 yd
3m
2m
5m
2 in.
2 in.
2 in.
10 in.
10 in.
2 in.
2 in.
2 in.
COORDINATE GEOMETRY Find the perimeter of each polygon.
10. triangle ABC with vertices A(3, 5), B(3, 1), and C(0, 1)
11. quadrilateral QRST with vertices Q(23, 2), R(1, 2), S(1, 24), and T(23, 24)
12. quadrilateral LMNO with vertices L(21, 4), M(3, 4), N(2, 1), and O(22, 1)
ALGEBRA Find the length of each side of the polygon for the given perimeter.
13. P 5 104 millimeters
14. P 5 84 kilometers
15. P 5 88 feet
4w 2 1
w
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Glencoe/McGraw-Hill
33
Glencoe Geometry
Lesson 1-6
Polygons
NAME ______________________________________________ DATE
1-6
____________ PERIOD _____
Practice
Polygons
Name each polygon by its number of sides and then classify it as convex or
concave and regular or irregular.
1.
2.
3.
Find the perimeter of each figure.
4.
7 mm
5.
18 mm
6.
21 mi
10 mm
18 mm
33 mi
14 cm
2 cm
6 cm
4 cm 6 cm
6 cm
4 cm
14 cm
32 mi
COORDINATE GEOMETRY Find the perimeter of each polygon.
7. quadrilateral OPQR with vertices O(23, 2), P(1, 5), Q(6, 4), and R(5, 22)
8. pentagon STUVW with vertices S(0, 0), T(3, 22), U(2, 25), V(22, 25), and W(23, 22)
ALGEBRA Find the length of each side of the polygon for the given perimeter.
9. P 5 26 inches
10. P 5 39 centimeters
11. P 5 89 feet
3x 1 5
6n 2 8
2x 1 2
2x 2 3
n
x19
5x 2 4
SEWING For Exercises 12–13, use the following information.
Jasmine plans to sew fringe around the scarf shown in the diagram.
12. How many inches of fringe does she need to purchase?
16 in.
4 in.
4 in.
16 in.
13. If Jasmine doubles the width of the scarf, how many inches of fringe will she need?
©
Glencoe/McGraw-Hill
34
Glencoe Geometry
NAME ______________________________________________ DATE
1-6
____________ PERIOD _____
Reading to Learn Mathematics
Pre-Activity
How are polygons related to toys?
Read the introduction to Lesson 1-6 at the top of page 45 in your textbook.
Name four different shapes that can each be formed by four sticks connected to
form a closed figure. Assume you have sticks with a good variety of lengths.
Reading the Lesson
1. Tell why each figure is not a polygon.
a.
b.
c.
2. Name each polygon by its number of sides. Then classify it as convex or concave and
regular or not regular.
a.
b.
c.
3. What is another name for a regular quadrilateral?
4. Match each polygon in the first column with the formula in the second column that can
be used to find its perimeter. (s represents the length of each side of a regular polygon.)
a. regular dodecagon
b. square
i. P 5 8s
ii. P 5 6s
c. regular hexagon
iii. P 5 a 1 b 1 c
d. rectangle
iv. P 5 12s
e. regular octagon
f. triangle
v. P 5 2, 1 2w
vi. P 5 4s
Helping You Remember
5. One way to remember the meaning of a term is to explain it to another person.
How would you explain to a friend what a regular polygon is?
©
Glencoe/McGraw-Hill
35
Glencoe Geometry
Lesson 1-6
Polygons