Download Perimeter, Circumference, and Area

1-8
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.
triangle
square
rectangle
circle
consecutive (adjective) kun SEK yoo tiv
Definition: Consecutive means following in order without interruption.
Related Word: sequence
Example: The numbers 2, 4, 6, 8, . . . are consecutive even numbers.
Non-Example: The numbers 1, 3, 2, 5, 4, . . . are NOT consecutive numbers.
Use Your Vocabulary
Draw a line from each sequence of letters in Column A to the next consecutive
letter in Column B.
Column A
Column B
3. L, M, N, O, . . .
R
4. V, U, T, S, . . .
I
5. A, C, E, G….
P
Chapter 1
30
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Vocabulary Builder
Key Concept Perimeter, Circumference, and Area
6. Label the parts of each of the figures below.
Square
P 5 4s
A5
s2
Triangle
Rectangle
Circle
P5a1b1c
P 5 2b 1 2h
C 5 pd or C 5 2pr
A 5 12bh
A 5 bh
A 5 pr2
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
in. by
in.
8. 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.
9. Solve using substitution.
10. The perimeter of the picture is
in.
Problem 2 Finding Circumference
Got It? What is the circumference of a circle with radius 24 m in terms of π?
11. Error Analysis At the right is one student’s solution. What error did the
student make?
_________________________________________________________
_________________________________________________________
24 m
c = πd
c = π(24)
c = 24π
12. Find the correct circumference.
31
Lesson 1-8
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?
4
13. Graph the quadrilateral on the coordinate plane at the right.
3
2
14. Use the justifications at the right to find the length of each side.
JK 5 P 23 2 1 P
Use the Ruler Postulate.
1
Ľ5 Ľ4 Ľ3 Ľ2 Ľ1 O
Simplify.
5
KL 5 P 42
P
x
1
2
3
4
5
Ľ2
Ľ3
Use the Ruler Postulate.
Ľ4
Simplify.
5
JM 5 P 232
y
P
Ľ5
Use the Ruler Postulate.
Simplify.
5
ML 5
Ä
5
Ä
5
Ä
5
Ä
(1 2 (23))2 1 (4 2
(
)2 1 32
(
)1(
(
)
)2
Use the Distance Formula.
Simplify within parentheses.
Simplify powers.
)
Add.
Take the square root.
5
JK 1 KL 1 JM 1 ML 5
16. The perimeter of JKLM is
1
1
1
5
units.
Problem 5 Finding Area of a Circle
Got It? The diameter of a circle is 14 ft. What is its area in terms of p?
17. Label the diameter and radius of the circle at the right.
18. Use the formula A 5
pr2
19. The area of the circle is
to find the area of the circle in terms of p.
p ft 2 .
Key Concept Postulate 1–10 Area Addition Postulate
20. The area of a region is the sum / difference of the areas of its nonoverlapping parts.
Chapter 1
32
ft
ft
Copyright © by Pearson Education, Inc. or its affiliates. All Rights Reserved.
15. Add the side lengths to find the perimeter.
Problem 6 Finding Area of an Irregular Shape
Got It? Reasoning The figure below shows one way to separate the figure at the
left. What is another way to separate the figure?
3 cm
A1
3 cm
3 cm
A2
9 cm
3 cm
6 cm
A3
3 cm
9 cm
21. Draw segments to show two different ways to separate the figure. Separate the
left-hand figure into three squares.
3 cm
3 cm
9 cm
9 cm
Copyright © by Pearson Education, Inc. or its affiliates. All Rights Reserved.
Lesson Check • Do you UNDERSTAND?
Compare and Contrast Your friend can’t remember whether 2pr computes the
circumference or the area of a circle. How would you help your friend? Explain.
22. Underline the correct word(s) to complete each sentence.
Area involves units / square units .
Circumference involves units / square units .
The formula 2pr relates to area / circumference because it involves units / square units .
Math Success
Check off the vocabulary words that you understand.
perimeter
area
Rate how well you can find the area of irregular shapes.
Need to
review
0
2
4
6
8
Now I
get it!
10
33
Lesson 1-8