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CHAPTER 9 Areas
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(c) If its area is 54 and the ratio of the base to the altitude is 3:2 (d) If its area is 12 and the perimeter is 16 (e) If its area is 70 and the base and altitude are represented by 2x and x 2
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(f) If its area is 160 and the base and altitude are represented by 3x 4 and x 9.4. Find the area of (a) a square yard in square inches; (b) a square meter in square decimeters (1 m 10 dm). (9.2)
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9.5. Find the area of a square if (a) a side has length 15; (b) a side has length 31; (c) a side has length 1.8; (d) a side 2 has length 8a; (e) the perimeter is 44; (f) the perimeter is 10; (g) the perimeter is 12b; (h) the diagonal has length 8; (i) the diagonal has length 9; (j) the diagonal has length 8 22. (9.2) 9.6. Find the area of a square if (a) the radius of the circumscribed circle is 8; (b) the diameter of the circumscribed circle is 12; (c) the diameter of the circumscribed circle is 10 22; (d) the radius of the inscribed circle is 31; 2 (e) the diameter of the inscribed circle is 20. (9.2) 9.7. If a floor is 20 m long and 80 m wide, how many tiles are needed to cover it if (a) each tile is 1 m2; (b) each tile is a square 2 m on a side; (c) each tile is a square 4 m on a side. (9.2) 9.8. If the area of a square is 81, find the length of (a) its side; (b) its perimeter; (c) its diagonal; (d) the radius of the inscribed circle; (e) the radius of the circumscribed circle. (9.2) 9.9. (a) Find the length of the side of a square whose area is 61. 4 (b) Find the perimeter of a square whose area is 169. (c) Find the length of the diagonal of a square whose area is 50. (d) Find the length of the diagonal of a square whose area is 25. (e) Find the radius of the inscribed circle of a square whose area is 144. (f ) Find the radius of the circumscribed circle of a square whose area is 32. 9.10. Find the area of a parallelogram if the base and altitude have lengths, respectively, of (a) 3 ft and 51 ft; (b) 4 ft 3 and 1 ft 6 in; (c) 20 and 3.5; (d) 1.8 m and 0.9 m. (9.3) 9.11. Find the area of a parallelogram if the base and altitude have lengths, respectively, of (a) 3x and x; (b) x 3 and x; (c) x 5 and x 5; (d) 4x 1 and 3x 2. (9.3) 9.12. Find the area of a parallelogram if (a) The area is represented by x2, the base by x (b) The area is represented by x
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(9.2)
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3, and the altitude by x 2
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10, the base by x, and the altitude by x 2 3, and the altitude by x 3 (9.3)
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(c) The area is represented by 2x2 34, the base by x 9.13. In a parallelogram, find
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(a) The base if the area is 40 and the altitude has length 15 (b) The length of the altitude if the area is 22 and the base has length 1.1
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CHAPTER 9 Areas
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(c) The length of the base if the area is 27 and the base is three times the altitude (d) The length of the altitude if the area is 21 and the base has length four more than the altitude (e) The base if the area is 90 and the ratio of the base to the altitude is 5:2 (f) The length of the altitude to a side of length 20 if the altitude to a side of length 15 is 16 (g) The length of the base if the area is 48, the base is represented by x by x 1 (h) The length of the base if the area is represented by x2 3, and the altitude is represented 1