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Lesson Menu Five-Minute Check (over Lesson 11–2) CCSS 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

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Over Lesson 11–2 5-Minute Check 1 A.202 units 2 B.198 units 2 C.62.7 units 2 D.28.4 units 2 Find the area of the figure. Round to the nearest tenth if necessary.

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Over Lesson 11–2 5-Minute Check 1 A.202 units 2 B.198 units 2 C.62.7 units 2 D.28.4 units 2 Find the area of the figure. Round to the nearest tenth if necessary.

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Over Lesson 11–2 5-Minute Check 2 A.96 units 2 B.92.4 units 2 C.83.1 units 2 D.81.8 units 2 Find the area of the figure. Round to the nearest tenth if necessary.

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Over Lesson 11–2 5-Minute Check 2 A.96 units 2 B.92.4 units 2 C.83.1 units 2 D.81.8 units 2 Find the area of the figure. Round to the nearest tenth if necessary.

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Over Lesson 11–2 5-Minute Check 3 A.70 units 2 B.72.5 units 2 C.75 units 2 D.77.5 units 2 Find the area of the figure. Round to the nearest tenth if necessary.

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Over Lesson 11–2 5-Minute Check 3 A.70 units 2 B.72.5 units 2 C.75 units 2 D.77.5 units 2 Find the area of the figure. Round to the nearest tenth if necessary.

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Over Lesson 11–2 5-Minute Check 4 A.58.5 units 2 B.117 units 2 C.198 units 2 D.234 units 2 Find the area of the figure. Round to the nearest tenth if necessary.

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Over Lesson 11–2 5-Minute Check 4 A.58.5 units 2 B.117 units 2 C.198 units 2 D.234 units 2 Find the area of the figure. Round to the nearest tenth if necessary.

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Over Lesson 11–2 5-Minute Check 5 A.6 units B.5 units C.4 units D.3 units Trapezoid LMNO has an area of 55 square units. Find the height.

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Over Lesson 11–2 5-Minute Check 5 A.6 units B.5 units C.4 units D.3 units Trapezoid LMNO has an area of 55 square units. Find the height.

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Over Lesson 11–2 5-Minute Check 6 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.

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Over Lesson 11–2 5-Minute Check 6 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.

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CCSS Content Standards G.C.5 Derive using similarity the fact that the length of the arc intercepted by an angle is proportional to the radius, and define the radian measure of the angle as the constant of proportionality; derive the formula for the area of a sector. G.GMD.1 Give an informal argument for the formulas for the circumference of a circle, area of a circle, volume of a cylinder, pyramid, and cone. Mathematical Practices 1 Make sense of problems and persevere in solving them. 6 Attend to precision

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Then/Now You found the circumference of a circle. Find areas of circles. Find areas of sectors of circles.

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Vocabulary sector of a circle segment of a circle

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Concept 1

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Example 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.

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Example 1 Area of a Circle Answer: Area of a circle Substitution Use a calculator.

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

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Example 1 A.62.8 ft 2 B.254.5 ft 2 C.314.2 ft 2 D.1256.6 ft 2 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.

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Example 1 A.62.8 ft 2 B.254.5 ft 2 C.314.2 ft 2 D.1256.6 ft 2 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.

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Example 2 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: Area of a circle Substitution Divide each side by . Simplify. 4.3 ≈ r Take the positive square root of each side. = r

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Example 2 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 square root of each side. = r

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Example 2 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.

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Example 2 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.

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Concept 2

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Example 3 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 1Find 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 2Find 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.

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Example 3 Area of a Sector Area of a sector x = 36 and r = 4.5 Use a calculator. Answer:

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Example 3 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.

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Example 3 A.16.21 in 2 B.19.24 in 2 C.26.43 in 2 D.38.48 in 2 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?

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Example 3 A.16.21 in 2 B.19.24 in 2 C.26.43 in 2 D.38.48 in 2 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?

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End of the Lesson

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