If Two Polygons Are Similar, Then Their Areas Are Proportional to the Square of the Scale Factor SOLUTION: Between Them

Chapter 10 Study Guide and Review

State whether each sentence is true or false. If 6. The measure of each radial angle of a regular n-gon false, replace the underlined term to make a is . true sentence. 1. The center of a trapezoid is the perpendicular SOLUTION: distance between the bases. false; central SOLUTION: ANSWER: false; height false; central ANSWER: 7. The apothem of a polygon is the perpendicular false; height distance between any two parallel bases.

2. A slice of pizza is a sector of a circle. SOLUTION: false; height of a parallelogram SOLUTION: true ANSWER: false; height of a parallelogram ANSWER: true 8. The height of a triangle is the length of an altitude drawn to a given base. 3. The center of a regular polygon is the distance from the middle to the circle circumscribed around the SOLUTION: polygon. true

SOLUTION: ANSWER: false; radius true

ANSWER: 9. Explain how the areas of two similar polygons are false; radius related.

4. The segment from the center of a square to the SOLUTION: corner can be called the radius of the square. If two polygons are similar, then their areas are proportional to the square of the scale factor SOLUTION: between them. true ANSWER: ANSWER: If two polygons are similar, then their areas are true proportional to the square of the scale factor 5. A segment drawn perpendicular to a side of a regular between them. polygon is called an apothem of the polygon.

SOLUTION: true

ANSWER: true

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10. Explain how to determine the center of a regular polygon.

SOLUTION: The center of a regular polygon is the center of its 12. circumscribed circle. SOLUTION: ANSWER: The center of a regular polygon is the center of its circumscribed circle.

Find the perimeter and area of each parallelogram or triangle. Round to the nearest tenth if necessary.

ANSWER: P = 38.4 in.; A = 70 in2 11.

SOLUTION:

13.

SOLUTION:

ANSWER: Use the Pythagorean Theorem to find the length of P = 50 cm; A = 60 cm2 the third side of the triangle.

The perimeter is about 3.6 + 3 + 3.6 = 13.2 mm.

ANSWER: P = 13.2 mm; A = 6 mm2 eSolutions Manual - Powered by Cognero Page 2 Chapter 10 Study Guide and Review

Find the area of each trapezoid, rhombus, or kite.

14.

SOLUTION:

16.

SOLUTION:

The perimeter is 12 + 9 + 15 = 36 ft.

ANSWER: P = 36 ft; A = 54 ft2 ANSWER: 15. PAINTING Two of the walls of an attic in an A- 84 ft2 frame house are triangular, each with a height of 12 feet and a width of 22 feet. How much paint is needed to paint one end of the attic?

SOLUTION:

17.

SOLUTION:

ANSWER: 132 sq. ft

ANSWER: 96 cm2

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Find the area of each shaded sector. Round to the nearest tenth.

18.

SOLUTION: 21. SOLUTION:

ANSWER: 168 ft2

ANSWER: 1.5 m2

19.

SOLUTION: 22.

SOLUTION:

ANSWER: 336 cm2

20. KITES Team Dragon’s kite is 4 ft long and 3 ft across. How much fabric does it take to make their kite? ANSWER: 175.8 in2 SOLUTION:

ANSWER: 6 ft2

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24. PIZZA Charlie and Kris ordered a 16-inch pizza and 23. BICYCLES A bicycle tire decoration covers of cut the pizza into 12 slices. the circle formed by the tire. If the tire has a a. If Charlie ate 3 pieces, what area of the pizza did diameter of 26 inches, what is the area of the he eat? decoration? b. If Kris ate 2 pieces, what area of the pizza did she eat? SOLUTION: c. What is the area of leftover pizza?

SOLUTION: a.

ANSWER: 59 in2

ANSWER: a. 50.27 in2 b. 33.51 in2 c. 117.29 in2

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Find the area of each figure. Round to the nearest tenth.

26.

SOLUTION: 25. A regular octagon has 8 congruent triangles with 8 SOLUTION: congruent central angles, so the measure of each A regular hexagon has 6 congruent triangles and 6 central angle is 360 ÷ 8 = 45. congruent central angles, so the measure of each central angle is = 60.

Apothem is the height of the isosceles triangle ABC and it splits the triangle into two congruent triangles.

Apothem is the height of equilateral triangle ABC and splits the triangle into two congruent Use the trigonometric ratios to find the side length triangles. and apothem of the polygon.

Use the Trigonometric ratios to find the apothem of the polygon.

AB = 2(AD) = 12 sin 22.5

ANSWER: ANSWER: 101.8 cm2 166.3 ft2

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27.

SOLUTION: 28. A regular hexagon has 6 congruent triangles with 6 congruent central angles, so the measure of each SOLUTION: central angle is 360 ÷ 6 = 60.

Apothem is the height of an equilateral triangle Area of the polygon = Area of the rectangle + Area ABC and it splits the triangle into 2 congruent of the semicircle triangles.

Use the trigonometric ratios to find the side length ANSWER: and apothem of the polygon.

ANSWER: 65.0 m2

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29. JEWELRY What is the area of the pendant shown For each pair of similar figures, use the given below? Round to the nearest hundredth. areas to find the scale factor from the blue to the green figure. Then find x.

30.

SOLUTION: The scale factor between the blue triangle and the SOLUTION: green triangle is , so the ratio of their areas is

The pendant is composed of three figures: a rhombus, a circle and a square. Determine the area of each figure:

The total area of the pendant is 0.75 + 0.79 + 6.125 = 7.66 cm² The scale factor is or . ANSWER: 7.66 cm² ANSWER:

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31. 32.

SOLUTION: SOLUTION: The scale factor between the blue triangle and the The scale factor between the blue triangle and the

green triangle is , so the ratio of their areas is green triangle is , so the ratio of their areas is

. .

The scale factor is or . The scale factor is or . ANSWER: ANSWER:

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COORDINATE GEOMETRY Find the area of 34. each figure. Use the segment length given to find the area of a similar polygon. 33.

SOLUTION:

JM = ML = LK = KJ = 5. Area of the square JKLM = 5(5) = 25

Area of a triangle K'L' = 15 The scale factor between JKLM and J'K'L'M' is Area of triangle , so the ratio of their areas is . The scale factor between and is

or , so the ratio of their areas is .

ANSWER: area of JKLM = 25 square units; area of J'K'L'M' ≈ 225 square units

ANSWER: area of square units; area of square units

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35. LAND OWNERSHIP Joshua’s land is 600 square miles. He purchases an additional plot that is half the length and one-fourth the width of his original plot. 37. What is the new area of his land? SOLUTION: SOLUTION: Lateral Area = 2(3 ft + 7 ft)(8 ft) = 160 ft² The area of the original plot of land is 600 square miles. Therefore, . The area of the Surface Area = 2(3 ft)(7 ft) + 2(3 ft)(8 ft) + 2(7 ft)(8 additional plot of land is of the original plot. ft) = 202 ft² Simplify this to . Since , substitute this value in to the expression for the ANSWER: additional plot of land: Find the lateral area and surface area of each

cylinder. Round to the nearest tenth if necessary.

38. SOLUTION: Therefore, the area of his new land would be 600 + 75 = 675 mi². Lateral Area =

ANSWER: Surface Area = 675 mi²

Find the lateral area and surface area of each ANSWER: prism. Round to the nearest tenth if necessary. 125.7 in.²; 226.2 in.²

36.

SOLUTION: Lateral Area = 2(2 cm)(3 cm) + 2(3 cm)(11 cm) = 78 39. cm² SOLUTION:

Surface Area = 2(2 cm)(3 cm) + 2(3 cm)(11 cm) + Lateral Area = 2(2 cm)(11 cm) = 122 cm² Surface Area =

ANSWER: Sample answer: 78 cm²; 122 cm² ANSWER: 113.1 cm²; 169.6 cm²

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Find the lateral area and surface area of each figure. Round to the nearest tenth if necessary.

40.

SOLUTION: Lateral Area = 0.5(4)(3 m)(6 m) = 36 m² Surface Area = 0.5(4)(3 m)(6 m) + (3 m)(3 m) = 45 m²

ANSWER: 36 m²; 45 m²

41.

SOLUTION: First, find the slant height.

Lateral Area = Surface Area =

ANSWER: 354.4 cm²; 432.9 cm²