Five-Minute Check (over Lesson 11–2)

NGSSS

Then/Now

New Vocabulary

Key Concept: Area of a Circle

Example 1: Real-World Example: Area of a Circle

Example 2: Use the Area of a Circle to Find a Missing Measure

Key Concept: Area of a Sector

Example 3: Real-World Example: Area of a Sector

Over Lesson 11–2

A. A

B. B

C. C

D. D A B C D

0% 0%0%0%

A. 202 units2

B. 198 units2

C. 62.7 units2

D. 28.4 units2

Find the area of the figure. Round to the nearest tenth if necessary.

Over Lesson 11–2

A. A

B. B

C. C

D. D A B C D

0% 0%0%0%

A. 96 units2

B. 92.4 units2

C. 83.1 units2

D. 81.8 units2

Find the area of the figure. Round to the nearest tenth if necessary.

Over Lesson 11–2

A. A

B. B

C. C

D. D A B C D

0% 0%0%0%

A. 70 units2

B. 72.5 units2

C. 75 units2

D. 77.5 units2

Find the area of the figure. Round to the nearest tenth if necessary.

Over Lesson 11–2

A. A

B. B

C. C

D. D A B C D

0% 0%0%0%

A. 58.5 units2

B. 117 units2

C. 198 units2

D. 234 units2

Find the area of the figure. Round to the nearest tenth if necessary.

Over Lesson 11–2

A. A

B. B

C. C

D. D A B C D

0% 0%0%0%

A. 6 units

B. 5 units

C. 4 units

D. 3 units

Trapezoid LMNO has an area of 55 square units. Find the height.

Over Lesson 11–2

A. A

B. B

C. C

D. D A B C D

0% 0%0%0%

A. 4 m

B. 8 m

C. 16 m

D. 1800 m

The area of a kite is 120 square meters. The length of one diagonal is 15 meters. Find the length of the other diagonal.

MA.912.G.2.6 Use coordinate geometry to prove properties of congruent, regular and similar polygons, and to perform transformations in the plane.

MA.912.G.6.5 Solve real-world problems using measures of circumference, arc length, and areas of circles and sectors.

Also addresses MA.912.G.8.2 and MA.912.G.8.3.

You found the circumference of a circle. (Lesson 10–1)

• Find areas of circles.

• Find areas of sectors of circles.

• sector of a circle

• segment of a circle

Area of a Circle

MANUFACTURING An outdoor accessories company manufactures circular covers for outdoor umbrellas. If the cover is 8 inches longer than the umbrella on each side, find the area of the cover in square inches.

The diameter of the umbrella is 72 inches, and the cover must extend 8 inches in each direction. So the diameter of the cover is 8 + 72 + 8 or 88 inches. Divide by 2 to find that the radius is 44 inches.

Area of a Circle

Answer: The area of the cover is about 6082 square inches.

Area of a circle

Substitution

Use a calculator.

A. A

B. B

C. C

D. D A B C D

0% 0%0%0%

A. 62.8 ft2

B. 254.5 ft2

C. 314.2 ft2

D. 1256.6 ft2

A swimming pool company manufactures circular covers for above ground pools. If the cover is 1 foot longer than the pool on each side, find the area of the cover.

Use the Area of a Circle to Find a Missing Measure

ALGEBRA Find the radius of a circle with an area of 58 square inches.

Answer: The radius of the circle is about 4.3 in.

Area of a circle

Substitution

Divide each side by .

Simplify.4.3 ≈ r

Take the positive squareroot of each side.= r

A. A

B. B

C. C

D. D A B C D

0% 0%0%0%

A. 3.8 in.

B. 4.5 in.

C. 5.7 in.

D. 7.6 in.

ALGEBRA Find the radius of a circle with an area of 45 square inches.

Area of a Sector

PIE A pie has a diameter of 9 inches and is cut into 10 congruent slices. What is the area of one slice to the nearest hundredth?

Step 1 Find the arc measure of a pie slice.

Since the pie is equally divided into 10 slices, each slice will have an arc measure of 360 ÷ 10 or 36.

Step 2 Find the radius of the pie. Use this measureto find the area of the sector, or slice.

The diameter is 9 inches, so the radius is4.5 inches.

Area of a Sector

Area of a sector

x = 36 and r = 4.5

Use a calculator.

Answer: The area of one slice of pie is about 6.36 square inches.

A. A

B. B

C. C

D. D A B C D

0% 0%0%0%

A. 16.21 in2

B. 19.24 in2

C. 26.43 in2

D. 38.48 in2

PIZZA A pizza has a diameter of 14 inches and is cut into 8 congruent slices. What is the area of one slice to the nearest hundredth?