1. Find the area of a circle with the given measure.
2. Radius: 1 3 mi
1. Radius: 8 cm
ANSWER
about cm2
ANSWER
about 5.59 mi2
4. Solve x2 =
100 π .
3. Circumference: 4π ft
ANSWER
4π ft2
ANSWER
about _ +
5.64

2. Vocabulary
Sector of a circle – the region bounded by two radii of the circle and their intercepted arc
Area of a Sector Theorem 11.2 –
area of sector : area of circle = arc measure : 360

3. Use the formula for area of a circle
EXAMPLE 1
Use the formula for area of a circle
Find the indicated measure.
SOLUTION
a. Area
r = 2.5 cm
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.
ANSWER

4. Use the formula for area of a circle
EXAMPLE 1
Use the formula for area of a circle
Find the indicated measure.
SOLUTION
A = cm2
b. Diameter
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 centimeters.
ANSWER

5. Find the areas of the sectors formed by UTV.
EXAMPLE 2
Find areas of sectors
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°.
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.

6. Area of large sector = πr2 mUSV 360°
EXAMPLE 2
Find areas of sectors
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.
ANSWER

7. GUIDED PRACTICE
for Examples 1 and 2
Use the diagram to find the indicated measure.
about ft2
ANSWERS
1. Area of D
Area of red sector
about ft2
Area of blue sector
about ft2

8. Use the Area of a Sector Theorem
EXAMPLE 3
Use the Area of a Sector Theorem
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.
ANSWER

9. EXAMPLE 4
Standardized Test Practice
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.

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

11. GUIDED PRACTICE
for Examples 3 and 4
4. Find the area of H.
5. Find the area of the figure.
about cm2
ANSWER
about m2
ANSWER

12. GUIDED PRACTICE
for Examples 3 and 4
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 m =
360
π r2
360A .
ANSWER

13. Daily Homework Quiz
Find the area of the sectors formed by DEF.
Use the area of the
sector to find the area
of R
ANSWER
in.2,
in.2
ANSWER
cm2

14. Daily Homework Quiz
3. Find the area of the shaded region.
ANSWER
23.18 ft2