1. Fluency- Integers
Course X, Lesson X-X

2. Answers
Course X, Lesson X-X

3. HOW are the circumference and area of a circle related?
Geometry
HOW are the circumference and area of a circle related?
Course 2, Inquiry Lab before Lesson 8-2

4. Mathematical Practices
Geometry
7.G.B.3 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.
6 Attend to precision.
Course 2, Inquiry Lab before Lesson 8-2 Common Core State Standards © Copyright National Governors Association Center for Best Practices and Council of Chief State School Officers. All rights reserved.

5. Let’s develop a formula for finding the area of a circle.
Geometry
Mrs. Allende wants to create a family message center on a wall in her house. There are 4 family members, including Mrs. Allende. She decides to paint 1 circle for each family member using magnetic paint. Each circle will have a 12-inch radius. How do you find the area of a circle?
Let’s develop a formula for finding the area of a circle.
Fold a paper plate in half four times to divide it into 16 equal sections
Activity Continued 
Course 2, Inquiry Lab before Lesson 8-2

6. Let’s develop a formula for finding the area of a circle.
Geometry
Mrs. Allende wants to create a family message center on a wall in her house. There are 4 family members, including Mrs. Allende. She decides to paint 1 circle for each family member using magnetic paint. Each circle will have a 12-inch radius. How do you find the area of a circle?
Let’s develop a formula for finding the area of a circle.
Label the radius r as shown. Let C represent the circumference of the circle.
Activity Continued 
Course 2, Inquiry Lab before Lesson 8-2

7. Base: ______________________ Height: _____________________
Geometry
Mrs. Allende wants to create a family message center on a wall in her house. There are 4 family members, including Mrs. Allende. She decides to paint 1 circle for each family member using magnetic paint. Each circle will have a 12-inch radius. How do you find the area of a circle?
Let’s develop a formula for finding the area of a circle.
Cut out each section. Reassemble the sections to form a parallelogram-shaped figure.
What expressions represent the measurements of the base and the height?
Base: ______________________ Height: _____________________
Substitute these values into the formula for the area of a parallelogram, A = b x h. Write the new formula. ___________________________________
Replace C with the expression for the circumference of a circle, 2 r. Simplify the equation and describe what it represents. ________________________________
_________________________________________________________________
Course 2, Inquiry Lab before Lesson 8-2

8. HOW are the circumference and area of a circle related?
Geometry
HOW are the circumference and area of a circle related?
Course 2, Inquiry Lab before Lesson 8-2

9. 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.
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

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

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

12. Mathematical Practices
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.
Course 2, Lesson Common Core State Standards © Copyright National Governors Association Center for Best Practices and Council of Chief State School Officers. All rights reserved.

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

14. Geometry
semicircle
Course 2, Lesson 8-2

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

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

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

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

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

20. The radius is (24) or 12 millimeters.
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. 1
The radius is (24) or 12 millimeters. 2
A = πr2
Area of a circle
A ≈ 3.14 • 122 3
Replace r with 12.
A ≈ 4
Multiply.
The area is approximately square millimeters. 5
Need Another Example?

21. 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
Answer

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

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

24. On a basketball court, there is a semicircle above the
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.
A = πr2 1
Area of a semicircle 2
A ≈ 0.5(3.14)(62)
Replace π with 3.14 and r with 6.
A ≈ 0.5(3.14)(36) 3
62 = 6 • 6 = 36 4
A ≈ 56.5
Multiply.
So, the area of the semicircle is approximately 56.5 square feet. 5
Need Another Example?

25. 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
Answer

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

27. How did what you learned today help you answer the
Geometry
How did what you learned
today help you answer the
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
Course 2, Lesson 8-2

28. Geometry
Functions
Ratios and Proportional Relationships
Suppose you have a circular rug in your living room that measures 5 feet in diameter. Find the area of the rug. Round to the nearest hundredth.
Course 2, Lesson 8-2