1. Areas of Circles and Sectors
Warm Up
Lesson Presentation
Lesson Quiz

2. Warm-Up
Find the area of a circle with the given measure.
1. Radius: 8 cm
ANSWER
about cm2
2. Radius: 1 3 mi
ANSWER
about 5.59 mi2

3. Warm-Up
Find the area of a circle with the given measure.
3. Circumference: 4π ft
ANSWER
4π ft2
4. Solve x2 =
100 π .
ANSWER
about _ +
5.64

4. Find the indicated measure. a. Area
Example 1
Find the indicated measure.
a. Area
r = 2.5 cm
SOLUTION
A = πr2
Write formula for the area of a circle.
= π (2.5)2
Substitute 2.5 for r.
= 6.25π
Simplify.
≈ 19.63
Use a calculator.
The area of A is about square centimeters.

5. Find the indicated measure. b. Diameter
Example 1
Find the indicated measure.
b. Diameter
A = cm2
SOLUTION
A = πr2
Write formula for the area of a circle.
= πr2
Substitute for A.
= r2
113.1 π
Divide each side by π.
≈ r
Find the positive square root of each side.
The radius is about 6 cm, so the diameter is about 12 cm.

6. Example 2
Find the areas of the sectors formed by UTV.
SOLUTION
STEP 1
Find the measures of the minor and major arcs.
Because m UTV = 70°, mUV = 70° and
mUSV = 360° – 70° = 290°.

7. Find the areas of the small and large sectors.
Example 2
STEP 2
Find the areas of the small and large sectors.
Area of small sector = πr2
mUV
360°
Write formula for area
of a sector.
= π 82
70°
360°
Substitute.
≈ 39.10
Use a calculator.
Area of large sector = πr2
mUSV
360°
Write formula for area
of a sector.
= π 82
290°
360°
Substitute. ≈
Use a calculator.
The areas of the small and large sectors are about square units and square units, respectively.

8. Guided Practice
Use the diagram to find the indicated measure.
1. Area of D
about ft2
ANSWER
2. Area of red sector
about ft2
ANSWER
3. Area of blue sector
about ft2.
ANSWER

9. Use the diagram to find the area of V.
Example 3
Use the diagram to find the area of V.
SOLUTION
Area of sector TVU = Area of V
mTU
360°
Write formula for
area of a sector.
35 = Area of V
40°
360°
Substitute.
315 = Area of V
Solve for Area of V.
The area of V is 315 square meters.

10. Example 4
SOLUTION
The area you need to paint is the area of the rectangle minus the area of the entrance. The entrance can be divided into a semicircle and a square.

11. Example 4
180°
= (26) – (π ) + 162
360°
= 936 – [32π ] ≈
The area is about 579 square feet.
The correct answer is C.
ANSWER

12. Guided Practice
4. Find the area of H.
about cm2
ANSWER

13. Guided Practice
5. Find the area of the figure.
about m2
ANSWER

14. Guided Practice
6. If you know the area and radius of a sector of a circle, can you find the measure of the intercepted arc? Explain.
Yes; the formula for the area of sector is m
A = and if you solve this for m, you get
360
π r2
360A .
ANSWER

15. Lesson Quiz
1. Find the area of the sectors formed by DEF.
ANSWER
in.2, in.2

16. Lesson Quiz
2. Use the area of the sector to find the area
of R
ANSWER
cm2

17. Lesson Quiz
3. Find the area of the shaded region.
ANSWER
23.18 ft2