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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 Lesson Menu

Find the area of the figure. Round to the nearest tenth if necessary. A. 202 units2 B. 198 units2 C. 62.7 units2 D. 28.4 units2 A B C D 5-Minute Check 1

Find the area of the figure. Round to the nearest tenth if necessary. A. 96 units2 B. 92.4 units2 C. 83.1 units2 D. 81.8 units2 A B C D 5-Minute Check 2

Find the area of the figure. Round to the nearest tenth if necessary. A. 70 units2 B. 72.5 units2 C. 75 units2 D. 77.5 units2 A B C D 5-Minute Check 3

Find the area of the figure. Round to the nearest tenth if necessary. A. 58.5 units2 B. 117 units2 C. 198 units2 D. 234 units2 A B C D 5-Minute Check 4

Trapezoid LMNO has an area of 55 square units. Find the height. A. 6 units B. 5 units C. 4 units D. 3 units A B C D 5-Minute Check 5

The area of a kite is 120 square meters The area of a kite is 120 square meters. The length of one diagonal is 15 meters. Find the length of the other diagonal. A. 4 m B. 8 m C. 16 m D. 1800 m A B C D 5-Minute Check 6

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

You found the circumference of a circle. (Lesson 10–1) Find areas of circles. Find areas of sectors of circles. Then/Now

sector of a circle segment of a circle Vocabulary

Concept 1

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. Example 1

Answer: The area of the cover is about 6082 square inches. Area of a Circle Area of a circle Substitution Use a calculator. Answer: The area of the cover is about 6082 square inches. Example 1

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. A B C D A. 62.8 ft2 B. 254.5 ft2 C. 314.2 ft2 D. 1256.6 ft2 Example 1

ALGEBRA Find the radius of a circle with an area of 58 square inches. 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. Area of a circle Substitution Divide each side by . Take the positive square root of each side. = r Simplify. 4.3 ≈ r Answer: The radius of the circle is about 4.3 in. Example 2

ALGEBRA Find the radius of a circle with an area of 45 square inches. A. 3.8 in. B. 4.5 in. C. 5.7 in. D. 7.6 in. A B C D Example 2

Concept 2

Step 1 Find the arc measure of a pie slice. 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 measure to find the area of the sector, or slice. The diameter is 9 inches, so the radius is 4.5 inches. Example 3

Answer: The area of one slice of pie is about 6.36 square 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. Example 3

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? A. 16.21 in2 B. 19.24 in2 C. 26.43 in2 D. 38.48 in2 A B C D Example 3

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