1-8
PART 1
Perimeter, Circumference,
and Area
Vocabulary
Review
1. Cross out the shapes that are NOT polygons.
2. Write the name of each figure. Use each word once.
square
circle
rectangle
rectangle
circle
square
triangle
Vocabulary Builder
perimeter
perimeter (noun) puh RIM uh tur
Definition: The word perimeter comes from the Greek peri-, which
means “around,” and metron, which means “measure.” Perimeter
is the distance around a figure.
Math Usage: Perimeter is the sum of the lengths of the sides of a polygon or the
length of a closed curve, such as a circle.
Use Your Vocabulary
Draw a line from each word in Column A to its definition in Column B.
Column A
Column B
3. circumference
distance around a polygon
4. perimeter
number of square units in a figure
5. area
distance around a circle
Chapter 1
62
Copyright © by Pearson Education, Inc. or its affiliates. All Rights Reserved.
triangle
Key Concept Perimeter and Circumference
6. Label the parts of each of the figures below.
Square
Triangle
a
s
Rectangle
c
Circle
h
b
s
P 5 4s
r
C
h
d
b
P5a1b1c
P 5 2b 1 2h
C 5 pd or C 5 2pr
Problem 1 Finding the Perimeter of a Rectangle
Got It? You want to frame a picture that is 5 in. by 7 in. with a 1-in.-wide frame.
What is the perimeter of the picture?
7. The picture is 5 in. by 7
in.
8. Do you need to find the perimeter of the ouside frame?
Yes / No
9. Circle the formula that gives the perimeter of the picture.
P 5 4s
P 5 2b 1 2h
P5a1b1c
C 5 pd
Copyright © by Pearson Education, Inc. or its affiliates. All Rights Reserved.
10. Solve using substitution.
P5
5
5
5
2b 1 2h
2(5) 1 2(7)
10 1 14
24
11. The perimeter of the picture is 24 in.
Problem 2 Finding Circumference
Got It? What is the circumference of a circle with radius 24 m in terms of π?
12. Error Analysis At the right is one student’s solution. What error did the
student make?
Answers may vary. Sample: The student used a diameter
_________________________________________________________
of 24 m instead of a radius of 24 m.
_________________________________________________________
24 m
c = πd
c = π(24)
c = 24π
13. Find the correct circumference.
C 5 2πr
5 2π(24)
5 48π
63
Lesson 1-8, Part 1
Problem 3
Finding Perimeter in the Coordinate Plane
Got It? Graph quadrilateral JKLM with vertices J(23, 23),
5
K(1, 23), L(1, 4), and M(23, 1). What is the perimeter of JLKM?
3
12. Use the justifications at the right to find the length of each side.
KL 5
JM 5
u 232
u
5
Å
4
5
Ľ3
K
Ľ5
Use the Ruler Postulate.
Use the Distance Formula.
5 Å( 4 )2 1 32
5
3
Ľ4
ML 5 Å(1 2 (23))2 1 (4 2 1 )2
Å
2
Simplify.
5 4
5
J
Simplify.
1
x
1
Ľ2
Use the Ruler Postulate.
7
1
Ľ5 Ľ4 Ľ3 Ľ2 Ľ1 O
Simplify.
u 42 23 u
5
2
M
Use the Ruler Postulate.
4
5
L
4
11. Graph the quadrilateral on the coordinate plane at the right.
JK 5 u 23 2 1u
y
Simplify within the parentheses.
16 1 9
Simplify powers.
25
Add.
Take the square root.
5
13. Add the side lengths to find the perimeter.
4
1
7
1
4
1
5 5 20
14. The perimeter of JKLM is 20 units.
Lesson Check • Do you UNDERSTAND?
What is the perimeter of a rectangle with base 3 in. and height 7 in.?
15. In the space below, draw a sketch of the
rectangle. Label each side with its length.
16. Circle the expression(s) that you
could use to find the perimeter.
317
2(3 1 7)
3171317
7 in.
3 in.
3 in.
7 in.
17. The perimeter of the rectangle is 20 in.
Chapter 1
64
2?3?7
3?7
Copyright © by Pearson Education, Inc. or its affiliates. All Rights Reserved.
JK 1 KL 1 JM 1 ML 5