Math Geometry Chapter 11 Solutions Key

Geometry CP Chapter 11 Test Review Name: Kay Find the area of the shaded figure shown. 1. A = 4(15)² + π(15)² A = 900π + 900 A ≈ 2279.91 2. A = 35² + π(21)² A = 1225 + 441π A ≈ 1784.4 3. A = ½(55)(42 + 12) A = 1485 4. A = 32² + π(14)² A = 1024 + 196π A ≈ 1624.5 5. A = π(20)² + 2(21)(20) A = 400π + 840 A ≈ 2105.5 m² 6. A = ½(14)(17 + 23) A = 280 7. A = 12(40) + 12(40) A = 480 + 480 A = 960 in² 8. A = ½bh A = ½(6)(8) A = 24 in² 9. d₁ = 12 d₂ = 8√3 A = ½(12)(8√3) A = 48√3 ≈ 83.14 Find the unknown area. 10. A = 54n ^ 2 6 11 (6 ^ 2)/(1b ^ 2) = 54/A 161 A = 384f * t ^ 2 11. A = 175m * m ^ 2 7 mm 10 mm A = 85.75m * m ^ 2 (10 ^ 2)/(7 ^ 2) = 175/A 12. Rectangles ABCD and EDGH are similar. The width of ABCD is 18 centimeters and the perimeter is 120 centimeters. The length of EFGH is 91 centimeters. Find the ratio of the areas of triangle ABC to the area of triangle DEF: D A P P = 120 6 P = 2(18) + 2x 120 = 36 + 2x 42 = x sidis 42/91 = 6/13 (6 ^ 2)/(13 ^ 2) = boxed 36 169 13. Find the lengths of the bases of the trapezoid whose height is 5 meters. One base is three times as long as the other base. The area is 70 square meters. h = 5 A = 70 6 3X A = 1/2 * h(b_{1} + b_{2}) 70 = 1/2 * (5)(x + 3x) 70 = 1/2 * (6)(4x) x = 7 bd( es ; Tand 21 The area of circle R is 295.52 square inches. The area of sector PRQ is 55 square inches. Find the indicated measure. 14. Radius of circle R A = 9r ^ 2 295.52 41 = boxed (pi * r ^ 2)/pi 16. m PQ r \approx 9.7 in 53/295.52 = x/360 mP Q simeq67^ 17. Length of arc PQ y/60.9 = 67/360 length PR = 11.3 R Find the exact area circle. 18. 2/8 * i*n_{e} A 15. Circumference of circle R C = 2pi*r C = 2pi(9.7) C \approx 60.9 in A = n * r ^ - 2 A = 71 * (3/8) ^ 2 A = 17 * 9/64 A= 9qT b4 iny 19. 3.7 cm A A= pi * r ^ - 2 - A= pi (3, 7) ^ 2- A = 13.6991 ^ - 1 20. The area of a circle is 654 square centimeters. Find the diameter. A = πr² 654 = πr² r ≈ 14.4 d = 2r d ≈ 2(14.4) d ≈ 28.8 cm Find the areas of the sectors formed by ∠ACB. (Find the area of the shaded and unshaded arcs.) 21. Shaded area = (360/360) * π(8)² = 64π ≈ 201.1 cm² Unshaded area = (300/360) * π(8)² = 53.3π ≈ 167.6 in² 22. Shaded area = (110/360) * π(12.8)² ≈ 157.3 mm² Unshaded area = (250/360) * π(12.8)² ≈ 357.4 mm² Use the diagram to find the indicated measure. 23. Find the area of OM. A = 36.07 cm² 24. Find the radius of OM. r ≈ 9.7 m 25. Find the diameter of OM. d ≈ 14.1 ft The area of circle V is 624.36 square meters. The area of sector SVT is 64.17 square meters. Find the indicated measure. 26. Radius of circle V A = πr² 624.36 = πr² r ≈ 14.1 m 27. Circumference of circle V C = 2πr C ≈ 2π(14.1) C ≈ 88.6 m 28. m∠STV 64.17 = (37/360) * πr² m∠STV = 37° 29. Length of ST Length of ST = (360/360) * πr Length of ST = 88.6 m 30. Perimeter of shaded region P = r + r + length ST P = 14.1 + 14.1 + 9.1 = 37.3 m 31. Perimeter of unshaded region P = r + r + length SPR P = 14.1 + 14.1 + 79.5 = 107.7 m Find the area of the shaded region. 32. Total shaded area = 3π(8)² + 3π(4)² Total shaded area = 192π + 48π = 240π 33. A = 3π(13)² A = 507π 34. Circle area = π(16)² = 256π Square area = 32² = 1024 Shaded area = 1024 - 256π ≈ 219.75 Find the measure of a central angle of a regular polygon with the given number of sides. 35. 15 sides 360°/15 = 24° 36. 25 sides 360°/25 = 14.4° 37. 32 sides 360°/32 = 11.25° 38. A regular octagon has a radius of 11.5 inches. What is the length of its apothem? cos 22.5° = a/11.5 a ≈ 10.62 39. Find the exact area of a hexagon with an apothem of 12. A = ½aP A = ½(12)(48√3) A = 288√3 In #40-43 Find the perimeter and area of the regular polygon. 40. A = ½aP A = ½(8.26)(60) A = 247.8 41. A = ½aP A = ½(6√3)(72) A = 216√3