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CHAPTER 10 Regular Polygons and the Circle
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(c) The length of the apothem if its radius is 12 (d) Its radius if the length of a side is 6 (e) The length of the apothem if the length of a side is 26 (f) Its radius if the length of the apothem is 3 23 (g) The length of a side if the length of the apothem is 30 (h) The perimeter if the length of the apothem is 5 23 10.10. In a square, find (a) The length of a side if the radius is 18 (b) The length of the apothem if the radius is 14 (c) The perimeter if the radius is 5 22 (d) The radius if the length of a side is 16 (e) The length of a side if the length of the apothem is 1.7 (f) The perimeter if the length of the apothem is 32 (g) The radius if the perimeter is 40 (h) The length of the apothem if the perimeter is 16 22 10.11. In an equilateral triangle, find (a) The length of a side if its radius is 30 (b) The length of the apothem if its radius is 28 (c) The length of an altitude if its radius is 18 (d) The perimeter if its radius is 2 23 (e) Its radius if the length of a side is 24 (f) The length of the apothem if the length of a side is 24 (g) The length of its altitude if the length of a side is 96 (h) Its radius if the length of the apothem is 21 (i) The length of a side if the length of the apothem is 23 (j) The length of the altitude if the length of the apothem is 31 3 (k) The length of the altitude if the perimeter is 15 (l) The length of the apothem if the perimeter is 54 10.12. (a) Find the area of a regular pentagon to the nearest integer if the length of the apothem is 15. (b) Find the area of a regular decagon to the nearest integer if the length of a side is 20. 10.13. Find the area of a regular hexagon, in radical form, if (a) the length of a side is 6; (b) its radius is 8; (c) the length of the apothem is 10 23. (10.6) 10.14. Find the area of a square if (a) the length of the apothem is 12; (b) its radius is 9 22; (c) its perimeter is 40. (10.6) (10.6) (10.5)
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CHAPTER 10 Regular Polygons and the Circle
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10.15. Find the area of an equilateral triangle, in radical form, if (a) The length of the apothem is 2 23. (b) Its radius is 6. (c) The length of the altitude is 4. (d) The length of the altitude is 12 23. (e) The perimeter is 6 23. (f) The length of the apothem is 4.
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10.16. If the area of a regular hexagon is 150 23, find (a) the length of a side; (b) its radius; (c) the length of the apothem. (10.6) 10.17. If the area of an equilateral triangle is 81 23, find (a) the length of a side; (b) the length of the altitude; (c) its radius; (d) the length of the apothem. (10.6) 10.18. Find the ratio of the perimeters of two regular polygons having the same number of sides if (a) The ratio of the sides is 1:8. (b) The ratio of their radii is 4:9. (c) Their radii are 18 and 20. (d) Their apothems have lengths 16 and 22. (e) The length of the larger side is triple that of the smaller. (f) The length of the smaller apothem is two-fifths that of the larger. (g) The lengths of the apothems are 20 22 and 15. (h) The circumference of the larger circumscribed circle is 22 times that of the smaller. 10.19. Find the ratio of the perimeters of two equilateral triangles if (a) the sides have lengths 20 and 8; (b) their radii are 12 and 60; (c) their apothems have lengths 2 23 and 6 23; (d) the circumferences of their inscribed circles are 120 and 160; (e) their altitudes have lengths 5x and x. (10.7) 10.20. Find the ratio of the lengths of the sides of two regular polygons having the same number of sides if the ratio of (10.7) their areas is (a) 25:1; (b) 16:49; (c) x2:4; (d) 2:1; (e) 3:y2; (f) x:18. 10.21. Find the ratio of the areas of two regular hexagons if (a) their sides have lengths 14 and 28; (b) their apothems have lengths 3 and 15; (c) their radii are 6 23 and 23; (b) their perimeters are 75 and 250; (e) the circumferences of the circumscribed circles are 28 and 20. (10.7) 10.22. Find the circumference of a circle in terms of p if (a) the radius is 6; (b) the diameter is 14; (c) the area is 25p; (d) the area is 3p. (10.8) 10.23. Find the area of a circle in terms of p if (a) the radius is 3; (b) the diameter is 10; (c) the circumference is 16p; (d) the circumference is p; (e) the circumference is 6p 22. (10.8) 10.24. In a circle, (a) find the circumference and area if the radius is 5; (b) find the radius and area if the circumference is 16p; (c) find the radius and circumference if the area is 16p. (10.8) 10.25. In a regular hexagon, find the circumference of the circumscribed circle if (a) the length of the apothem is 3 23; (b) the perimeter is 12; (c) the length of a side is 31. Also find the circumference of its inscribed circle if (d) the length 2 of the apothem is 13; (e) the length of a side is 8; (f) the perimeter is 6 23. (10.9)
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