Chapter 11 Review. Period:

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1 Chapter 11 Review Name: Period: 1. Find the sum of the measures of the interior angles of a pentagon. 6. Find the area of an equilateral triangle with side 1.. Find the sum of the measures of the interior angles in the figure. 7. An equilateral triangle has a side length of 3. Find its area. 8. The perimeter of an equilateral triangle is 18. Find its area. 9. Find the area of a regular decagon with side 6 cm. 3. How many triangles are formed by drawing diagonals from one vertex in the figure? Find the sum of the measures of the angles in the figure. 10. Find the area of a regular nonagon with radius 6 cm. 11. A regular hexagon has an apothem of 3 and a side length of 3. Its area is. 1. The floor of a gazebo is a regular 0-gon. If the apothem is 30 feet, find the length of each side to two decimal places. 4. A regular pentagon has five congruent interior angles. What is the measure of each angle? 5. In a farmer s hexagonal field, when interior angles are put in increasing order, each differs from the next by 5. Find the measure of each interior angle of the field to the nearest.1 degree.

2 13. The figures are similar. Find the missing values. P = 144 P =? 18. Maria needs to make a poster that is 1.5 m by 3 m for the big game. The cost of the paper is $1.75. Later she needs another poster with dimensions 0.75 m by 1.5 m. What is the paper for this poster likely to cost? 6 A =? 16 A = Two similar trapezoids have areas 108 cm and 48 cm. Find the ratio of similarity. 15. The area of a regular octagon is 45 cm. What is the area of a regular octagon with sides six times as large as the sides of the first octagon? 16. ΔABC and ΔA B C are similar triangles with AB 5 =. If the area of ΔABC is 80 square AB 4 units, find the area of ΔA BC. 19. Find the circumference of a circle with radius 9 cm. Use π If a circle has a radius of 5 inches, what is the circumference rounded to the nearest whole number? Use π A circle has a circumference of 49 meters. Find its radius.. A circle has a circumference of 34 meters. Find its diameter. 3. For a circle of radius 8 feet, find the arc length of a central angle of 60. Leave your answer in terms of π. 4. The circumference of a circle is 84π cm. Find the diameter, the radius, and the length of an arc of Quadrilaterals ABCD and ABCD are similar AB with AB = 5. If the area of ABCD is 115 square units, what is the area of ABCD? 5. Circle O has a radius of If m AOB is 11, then find the length of AB to one decimal place.

3 6. Given: O with OC AB. If OA = 7 and OC =, find the arc length of AB to two decimal places. Explain your reasoning. 33. Find the area of the shaded region Find the arc length of AB to two decimal places. 34. In this figure, each circle has a radius of 4 inches. What is the area of the portion outside the circles but inside the square? Express your answer in terms of π. 8. The tires of an automobile have a diameter of inches. If the wheels revolve ten times, how far does the automobile move? (Round the result to the nearest tenth of a foot.) 9. A vehicle travels 15.7 feet while its wheels revolve 16 times. Find the diameter of the wheels to the nearest inch. 16 in 35. The figure below represents the overhead view of a deck surrounding a hot tub. What is the area of the deck? Use π The radius of a circular garden is.8 m. Find the circumference. Use π m.1 m 31. Find the area of the circle with radius 15 cm. Use 3.14 for π. 3. Find the area:.5 m

4 36. Find the area of the shaded region. 40. Find the area of the shaded region. (Assume that the ends of the figure are semicircles.) 60 9 cm 41. A square is inscribed in a circle of radius 3. Find the area of the square. 37. Assume a regular polygon (such as a hexagon) is circumscribed by a circle. If the number of sides of the regular polygon increases, then what happens to the area of the segments between the circle and the new polygon? (Illustrate your reasoning by using the figure below.) 4. Find the probability that a point chosen at random on AD is on AL. A B C D L Given: m AB = 100, a = 5.14, r = 8.00 Find the area of the shaded region to two decimal places. 39. Each circle is tangent to the other two. If the diameter of the large circle is 8, the area of the shaded region is.

5 43. Find the probability that a point chosen at random on AL is on AD. A B C D L 44. If a point is selected at random, what is the probability that it will lie within the shaded rectangular region rather than the unshaded rectangular region? Half of a circle is inside a square and half is outside, as shown. If a point is selected at random inside the square, find the probability that the point is also inside the circle. r r 46. A square is inscribed inside a circle as shown. If a point is chosen at random inside the circle, find the probability that the point is also inside the square. r r

6 Reference: [ ] [1] 540 Reference: [ ] [14] 3 : Reference: [ ] [] 540 Reference: [ a] [15] 160 cm Reference: [ a] [3] 4, 70 Reference: [ ] [16] 15 sq. units Reference: [ ] [4] 108 Reference: [ ] [17] 18.4 sq. units Reference: [ ] [5] 57.5, 8.5, 107.5, 13.5, 157.5, Reference: [ ] [18] $0.44 Reference: [ ] [6] 36 3 sq. units Reference: [ ] [19] 56.5 cm Reference: [ ] [7] 3 3 sq. units Reference: [ a] [0] 31 in. Reference: [11..1.] [8] 9 3 sq. units Reference: [11...3] [9] 77.0 cm Reference: [11...4] [10] cm Reference: [11...8a] [11] 18 3 sq. units Reference: [11...9] [1] 9.50 ft Reference: [ a] [1] 7.8m Reference: [ b] [] 10.8 m Reference: [ ] [3] 8 3 π feet Reference: [ ] [4] 84 cm; 4 cm; π cm Reference: [ ] [5] 14.4 units Reference: [ ] [13] A = 180, P = 54

7 Reference: [ ] cos AOC = 7 m AOC m AOB = m AOC m AOB = m AB Arc length of AB = (π 7) F I [6] HG 360 K J Reference: [ ] [7].6 cm Reference: [ ] [8] 57.6 ft Reference: [ ] [9] 30 in. Reference: [ ] [30] m Reference: [ ] [31] cm Reference: [ a] [3] m Reference: [ ] [33] 300π 5 3 Reference: [ a] [34] 56-64π Reference: [ ] [35] m Reference: [ a] [36] 4.41 cm Reference: [ ] The area decreases. For example, if the number of sides of a regular hexagon is doubled, then the area of the polygon increases by six times the amount shown. Since the area of the polygon has increased, the area of the segments between the polygon and the circle must have decreased. [37] Reference: [ ] [38] 4.34 units Reference: [ a] [39] Reference: [ ] [40] 3 sq. units Reference: [ ] [41] 36 sq. units Reference: [ ] 8 [4] 15 Reference: [ ] 19 [43] 7 Reference: [ ] 11 [44] 14 Reference: [ ] π [45] 8

8 Reference: [ ] [46] π