Geometry Quiz Review 11 Key

Geometry C.P. Quiz Review Name: Key 1. A = l * w A = 11 * 11 A = 121 u² 2. A = 1/2 h(b₁ + b₂) A = 1/2 * 8.8 * (10.2 + 16) A = 115.28 u² 3. tan 50° = 21/x x ≈ 17.6 A = 1/2 * 21 * (11 + 28.6) A = 415.8 u² 4. d₁ = 5 + 4 = 9 d₂ = 2 + 8 = 10 A = 1/2 * d₁ * d₂ A = 1/2 * 9 * 10 A = 45 u² 5. d₁ = 16 + 15 = 31 d₂ = 22 + 24 = 46 A = 1/2 * d₁ * d₂ A = 1/2 * 31 * 46 A = 713 u² 6. d₁ = 18 + 7 = 25 d₂ = 22 + 24 = 46 A = 1/2 * d₁ * d₂ A = 1/2 * 25 * 46 A = 575 u² 7. tan 40° = x/16 x ≈ 13.4 d₁ = 26 + 24 = 50 d₂ = 16 + 13.4 = 29.4 A = 1/2 * d₁ * d₂ A = 1/2 * 50 * 29.4 A = 735 u² 8. d₁ = 10 d₂ = 15 + 13 = 28 A = 1/2 * d₁ * d₂ A = 1/2 * 10 * 28 A = 140 u² shaded area: 140 - 65 = 75 u² 9. sin 43° = h/26 h ≈ 17.7 A = 1/2 * 19 * 17.7 A ≈ 168.2 u² 10. cos 71° = h/5 h ≈ 1.6 A = 1/2 * 4 * 1.6 A ≈ 3.8 u² 11. sin 42° = x/3 x ≈ 2 A = 1/2 * 4 * 2 A = 4 u² 12. cos 42° = h/3 h ≈ 2.2 A = 1/2 * 4 * 2.2 A = 4.4 u² Use the given area to find the value of x. 13. Area = 399 in² 399 = x * 21 x = 19 153 = 17 * x x = 9 Area = 196 ft² 196 = 1/2 * 28 * x x = 14 Company Logo: A company has a logo that is in the shape of a rhombus. The company wants to put its logo on a sign outside the building. On the sign, the diagonals of the rhombus will be 72 and 36 inches long. Find the area of the logo.   A = 1/2 * d1 * d2 A = 1/2 * (72) * (36) = 1296 in² Algebra: The area of a triangle is 225 square units. The base of the triangle is twice the height. Find the base and the height.   b = 2h A = 1/2 * b * h 225 = 1/2 * 2h * h 225 = h² h = 15 u b = 30 u Algebra: The area of a parallelogram is 216 square centimeters. The height of the parallelogram is two thirds of the base. Find the base and the height. h = 2/3 * b A = b * h 216 = b * 2/3 * b 216 = 2/3 * b² b = 18 cm h = 12 cm Algebra: Find the lengths of the bases described. The height is 5 meters. One base is three times as long as the other. The area is 70 square meters. b1 = x b2 = 3x A = 1/2 * h * (b1 + b2) 70 = 1/2 * 5 * (x + 3x) 28 = 4x 7 = x Trigonometry: In ABCD, base AD is 25 units and AB is 12 units. Find the height and area of ABCD if m∠A = 30°. h = 6, x = 6√3 A = 25 * 6 A = 150 u² 21. Trigonometry: In DEFGH, base EF is 15 units and EF is 6√2 units. Find the height and area of DEFGH if m∠E is 45°. h = 6 A = b * h A = 15 * 6 A = 90 u² triangle with base 15 and hypotenuse 6√2, with a 45degree angle 22. Complete the table of ratios for similar polygons. | Ratio of corresponding side lengths | Ratio of perimeters | Ratio of areas   | |---|---|---| | 5:8 | 5:8 | 25:64 | | 4:7 | 4:7 | 16:49 | | 13:6 | 13:6 | 169:36 | | 60:18 = 11:3 | 11:3 | 121:9 | Corresponding lengths in similar figures are given. Find the ratios (shaded to unshaded) of the perimeters and areas. Find the unknown areas.   23. Sides: 14/20 = 7/10 Perimeters: 7/10 Areas: 49/100 24. Sides: 24/9 = 8/3 Perimeters: 8/3 Areas: 64/9 A = 1024 mm² A = 144 mm² Use the given area to find XY. 25. ABCD ~ WXYZ A = 135 in² A = 15 in² 15²/x² = 135/15 x² = 25 x = 5 in two similar parallelograms, EFGH and UVWXY 26. EFGH ~ UVWXY A = 198 cm² A = 378 cm² 8²/x² = 198/378 x² = 144 x = 12 cm 27. Kites RSTU and VWXY are similar. The area of RSTU is 162 square feet. The diagonals of VWXY are 32 feet long and 18 feet long. Find the area of VWXY. Then use the ratio of the areas to find the lengths of the diagonals A = 1/2 * (32) * (18) A = 288 ft² two similar kites, RSTU and VWXY d1²/32² = 162/288 d1² = 162 d1 = 13.5 ft d2²/18² = 162/288 d2² = 288 d2 = 17 ft 28. Regular octagon ABCDEFGH has a side length of 10 mm and an area of 160 square mm. Regular octagon JKLMNOPQ has a perimeter of 200mm. Find its area. Side = 200/8 = 25 A = 1000 mm² regular hexagon with side length 12 Using the given value, find the EXACT area of the following regular polygons. 29. Side = 12 a = 6√3 P = 12(6) = 72 A = 1/2 * a * P A = 1/2 * (6√3) * (72) A = 216√3 30. Radius = 8√3 x = 4√3 * √3 = 4 * 3 = 12 s = 12 P = 24(3) = 72 A = 1/2 * a * P A = 1/2 * (4√3) * (72) A = 144√3 Using the given value, find the APPROXIMATE area of the following regular polygons. 31. Apothem = 10 tan 36° = x/10 x ≈ 7.3 s = 14.6 P = 14.6 * 5 = 73 A = 1/2 * a * P A = 1/2 * 10 * 73 A ≈ 365 u² 32. Radius = 11 sin 25.7° = x/11 x ≈ 4.8 s = 9.6 P = 9.6 * 6 = 57.6 cos 25.7° = a/11 a ≈ 9.9 A = 1/2 * a * P A = 1/2 * 9.9 * 57.6 A ≈ 284 u² A regular polygon has one exterior angle that is 40° and the perimeter is 72cm. Find the area of the polygon. 360/40 = 9 sides s = 72/9 = 8 a = 11 A = 1/2 * a * P A = 1/2 * 11 * 72 A = 396 u²