Chapter 11. Area of Polygons and Circles

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1 Chapter 11 Area of Polygons and Circles

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3 11.1 & 11.2 Area of Parallelograms, Triangles, Trapezoids, Rhombi, and Kites Use your formula chart to find the formula for the Areas of the following Polygons Square A = Rectangle A = Parallelogram A = Kite Triangle A = Trapezoid A = Kite A = Rhombus A = Examples: Find the areas of the following figures:

4 Examples: Find x. A = 247.5mm 2

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9 11.3 Area of Circles & Sectors Area of a Circle A = Examples: Find the answer of each circle. Give answers in exact and approximate form rounded to the nearest hundredth. Find the radius of a circle with an area of 63.6 square feet. Round answer to the nearest hundredth.

10 Sectors of Circles: Find the area of the shaded and unshaded region of the circle. Give answers in exact and approximate form rounded to the nearest hundredth. A pie is baked in a pie plate that has a diameter of 9 inches. If the pie is cut into 6 congruent pieces, what is the area of each piece rounded to the nearest hundredth?

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13 Previous Next Lesson 3 Areas of Circles Name Period Date In Exercises 1 3, leave your answers in terms of. 1. If d 6.4 cm, A. 2. If A 529 cm 2, r. 3. If C 36 cm, A. In Exercises 4 11, round your answers to the nearest 0.01 unit. 4. If r 7.8 cm, A. 5. If A , C. 6. If d 3.12, A. For Exercises 7 and 8, refer to the figure of a circle inscribed in an equilateral triangle. 7. Find the area of the 8. Find the area of the inscribed circle. shaded region. 9. x 2 and y 1 are tangent lines. ABCD is a square. Find the area of the shaded region. y 1 C 14 cm B ( 2, 7) D A (6, 1) x A horse is tethered on a 20 ft rope. If the rope is lengthened to 25 ft, by what percentage does the horse s grazing area increase? 11. The three circles are tangent. Find the area of the shaded region. 5 cm 12. A running track is shaped like a rectangle with a semicircle on each of the shorter sides. The distance around the track is 1 mile (5280 ft). The straightaway is twice as long as the width of the field. What is the area of the field enclosed by the track to the nearest square foot? Width Straightaway Field

14 Previous Next Lesson 3 Any Way You Slice It Name Period Date In Exercises 1 6, find the area of the shaded region. Round your answers to the nearest 0.01 cm cm 7 cm 3 cm r 1 3 cm, r 2 6 cm, 6. and r 3 9 cm. 8 cm 12 cm r 2 r 3 r 1 12 cm Shaded area is 20 cm Shaded area is 14 cm 2. Find 9. Shaded area is 15 cm 2. Find r. r to the nearest 0.01 cm. Find OT to the nearest 0.01 cm. 144 r S T Q r O 10. Raul s dog, Spot, is tied with a 20 ft rope to the center of the back wall of the shed. See the diagram below. Over what area can Spot play, to the nearest square foot? A U Shed 12 ft 20 ft

15 11.4 Area of REGULAR Polygons and Composite Figures Regular Polygon: Using triangles, find the area of the regular pentagon. Apothem: Radius of a Polygon: Central Angle of a Polygon: Area of a Regular Polygon

16 Composite Figures:

17 Examples: Find the area of each shaded figure. Round to the nearest hundredth if necessary. 1) 2)

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22 11.5 Area of Similar Figures Length = Length = Ratio: Width = Width = Ratio: Perimeter = Perimeter = Ratio: Area = Area = Ratio: Areas of Similar Polygons:

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24 Chapter 11 Test Review

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29 STAARTM State of Texas Assessments of Academic Readiness A bh = 1 2 A A = 1 d d A = 1 ( b + b ) h ap = 1 2 S = 1 P 2 l S = 1 2 Pl + B l l V = 1 B 3 h V = r

30 STAARTM State of Texas Assessments of Academic Readiness Ax + By = C B A C 2x 60 x x 2 45 x 30 x 3 45 x

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