Chapter 8 Geometry Homework Answers

Sec 8.1 228 m² 41.85 cm² 8 yd 21 cm 91 ft² 182 m² 96 in.² 210 cm 11. 6 square units 12. 7 ½ square units 16. 2(4)(3) + 2(5.5)(3) = 57 m² 17. For a constant perimeter, area is maximized by a square. 100 m ÷ 4 = 25 m per side; A = 625 m² 23. 96 sq. units 500 cm² 26. a = 76°, b = 52°, c = 104°, d = 52°, e = 76°, f = 47°, g = 90°, h = 43°, k = 104°, m = 86°

Sec 8.2 20 cm² 49.5 m² 300 sq. units 60 cm² 6 cm 7 ft 30 ft 5 cm 16 m x = 3.6 ft, y = 10.8 ft 70 m 144 cm² a = 34°, b = 68°, c = 68°, d = 56°, e = 56°, f = 90°, g = 34°, h = 56°, m = 56°, n = 90°, p = 34° 30. 3^2.6^2/3.6.3.6

Sec 8.3 a) 121, 952 ft² b) 244 gal of base paint and 488 gal of finishing paint He should buy at least four rolls of wallpaper. (The area of each roll is 125 ft². The total surface area to be papered is 480 ft²). If paper is cut off at the corners is wasted, he’ll need 5 rolls. 1552 ft²; 776 ft² more surface area $760 220 terra cotta tiles, 1107 blue tiles; $ 1598.15 21 336 ft²; $1780 $384 (16 gal) 60 cm² by either method Because ΔAOB is isosceles, m‹A = 20° and m‹AOB = 140°. mAB = 140° and mCD = 82°. mAC = mBD because parallel lines intercept congruent arcs on a circle. (360°-140°-82°)/2 = 69° E

Sec 8.4 2092 cm² 74 cm 256 cm 33 cm² 63 cm 490 cm² 57.6 m 25 ft total surface area = 13,680 in.² = 95 ft²; cost = $8075 19. a) incenter b) orthocenter c) centroid

Sec 8.5 9π in.² 49π cm² 0.79 m² 3 cm √3 in. 0.5 m 36π in.² 7846 m² 25π – 48 or about 30.5 sq. units 100π – 128 or about 186 sq. units 4 times A ≈ πr² because the 100-gon almost completely fills the circle 456 cm² 36 ft² x = mDE = 2 · 24° = 48° 90° + 38° + 28° +28° ≠ 180°

Sec 8.6 6π cm² 64π/3 cm² 192π cm² (π – 2) cm² (48π + 32) cm² 33π cm² 75 100 see diagram a) (144 – 36π) cm²; 78.54% b) (144 – 36π) cm²; 78.54% c) (144 – 36π) cm²; 78.54% d) (144 – 36π) cm²; 78.54% 480 m² True. If 24π = (9π/360) · 2πr, then r = 48 cm True. If 360/n = 24, then n = 15 False. It could be a rhombus. True; Triangle Inequality Conjecture

Sec 8.7 150 cm² 4070 cm² 216 cm² 340 cm² 103.7 cm² 1187.5 cm² area of square + 4 · area of trapezoid + 4 · area of triangle $1570

Ch 8 Review parallelogram (B) triangle (A) trapezoid (C) kite (E) regular polygon (F) circle (D) sector (J) annulus (I) cylinder (G) cone (H) see diagram Construct an altitude from the vertex of an obtuse angle to the base. Cut off the right triangle and move it to the opposite side, forming a rectangle. Because the parallelogram’s area hasn’t changed, its area equals the area of the rectangle. Because the area of the rectangle is given by the formula A = bh, the area of the parallelogram is also given by A = bh. (see diagram) Make a copy of the trapezoid and put the two copies together to form a parallelogram with base b1 + b2 and height h. Thus the area of one trapezoid is given by the formula A = ½(b1 + b2)h. (see diagram)

Ch 8 Review cont’d 800 cm² 5990.4 cm² 60π cm² or 188.5 cm² 32 cm 15 cm 40° 153.9 cm² 72 cm² 30.9 cm² 300 cm² 940 cm² 1356 cm²