This document provides examples for calculating the area of circles and semicircles using the formulas for area of a circle (A = πr^2) and area of a semicircle (A = 1/2 * πr^2). It gives step-by-step workings for finding the area of various circles and semicircles using a value of 3.14 for π. Examples include finding the area of a circle with a diameter of 6 cm, a circle with radius of 11 ft, and the semicircle above a basketball free-throw line with radius of 6 ft.

1. Find the radius or diameter of each circle with the given
dimensions.
1. d = 6 cm
2. r = 11 ft
Find the circumference of each circle. Use 3.14 for π. Round to
the nearest tenth if necessary.
3. 4.
5. Charlotte has a trampoline in her backyard. The diameter of the
trampoline is 14 feet. What method can Charlotte use to find the
circumference of the trampoline?
Course 2, Lesson 8-2

2. Course 2, Lesson 8-2
ANSWERS
1. r = 3 cm
2. d = 22 ft
3. 31.4 cm
4. 40.8 in.
5. Multiply the diameter by π.

3. Geometry
Course 2, Lesson 8-2
HOW do measurements help you
describe real-world objects?

4. Course 2, Lesson 8-2 Common Core State Standards © Copyright 2010. National Governors Association Center for Best Practices and
Council of Chief State School Officers. All rights reserved.
Geometry
• 7.G.4
Know the formulas for the area and circumference of a circle and
use them to solve problems; give an informal derivation of the
relationship between the circumference and area of a circle.
Mathematical Practices
1 Make sense of problems and persevere in solving them.
3 Construct viable arguments and critique the reasoning of others.
4 Model with mathematics.

5. • To find the area of a circle
• To find the area of a semicircle
Course 2, Lesson 8-2
Geometry

6. Course 2, Lesson 8-2
Geometry
• semicircle

7. Course 2, Lesson 8-2
Geometry
Words The area A of a circle equals Model
the product of and the square
of its radius r.
Symbols A =

2
r

8. 1
Need Another Example?
2
3
4
Step-by-Step Example
1. Find the area of the circle.
Use 3.14 for π.
Area of a circleA = πr2
Check for Reasonableness
The area of the circle is approximately 12.56 square inches.
Estimate 3 × 2 × 2 = 12
A ≈ 3.14 • 22
A ≈ 3.14 • 4
A ≈ 12.56
Replace r with 2.
22 = 2 • 2 = 4
Multiply.
12.56 ≈ 12

9. Answer
Need Another Example?
Find the area of the circle. Use 3.14 for π.
50.24 cm2

10. 1
Need Another Example?
2
3
4
Step-by-Step Example
2. Find the area of a circle with a radius of 14 centimeters.
Use for π.
Area of a circleA = πr2
Check for Reasonableness
The area of the circle is approximately
616 square centimeters.
Estimate
28
1
616 ≈ 588
3 × 14 × 14 = 588
A ≈ • 142
A ≈ • 196
A ≈ • 196
A ≈ 616
Replace π with and r with 14.
142 = 14 • 14 = 196
Divide by the GCF, 7.
Multiply.

11. Answer
Need Another Example?
Find the area of a circle with a radius of 7
meters. Use for π.
154 m2

12. 1
Need Another Example?
2
3
4
5
Step-by-Step Example
3. Find the area of the face of the Virginia quarter with
a diameter of 24 millimeters. Use 3.14 for π. Round
to the nearest tenth if necessary.
The area is approximately 452.2 square millimeters.
The radius is (24) or 12 millimeters.
A = πr2 Area of a circle
A ≈ 3.14 • 122 Replace r with 12.
A ≈ 452.16 Multiply.

13. Answer
Need Another Example?
Find the area covered by the fountain. Use 3.14 for π.
Round to the nearest tenth if necessary.
21.2 m2

14. Need Another Example?
Step-by-Step Example
4. Find the area of the semicircle.
Use 3.14 for π. Round to the
nearest tenth.
1
2
3
4
5
A = πr2 Area of a semicircle
A ≈ (3.14)82 Replace r with 8.
A ≈ 0.5(3.14)(82) 82 = 8 • 8 or 64
A ≈ 100.5 Simplify.
The area of the semicircle is approximately 100.5 square inches.

15. Answer
Need Another Example?
Find the area of the semicircle. Use 3.14 for π.
Round to the nearest tenth if necessary.
31.8 cm2

16. 1
Need Another Example?
2
3
4
5
Step-by-Step Example
5. On a basketball court, there is a semicircle above the
free-throw line that has a radius of 6 feet. Find the area of
the semicircle. Use 3.14 for π. Round to the nearest tenth.
So, the area of the semicircle is approximately 56.5 square feet.
A = πr2 Area of a semicircle
A ≈ 0.5(3.14)(62) Replace π with 3.14 and r with 6.
A ≈ 0.5(3.14)(36) 62 = 6 • 6 = 36
A ≈ 56.5 Multiply.

17. Answer
Need Another Example?
Tarie is cutting material in the shape of semicircles for
her craft project. What is the area of the semicircle? Use
3.14 for π. Round to the nearest tenth if necessary.
100.5 in.2

18. How did what you learned
today help you answer the
Course 2, Lesson 8-2
Geometry
HOW do measurements help you
describe real-world objects?

19. How did what you learned
today help you answer the
Course 2, Lesson 8-2
Geometry
HOW do measurements help you
describe real-world objects?
Sample answers:
• To find the area of a circular object, such as the area of
a radio signal
• To find the area of a semicircular object, such as
window

20. Suppose you have a circular
rug in your living room. Describe
how you would find the area
of the rug and which measures
you would need to know
in order to find its area.
Course 2, Lesson 8-2
Ratios and Proportional RelationshipsFunctionsGeometry