47. 1. Surveying A surveyor measured one side and two angles of a field, as shown in the diagram. Use a ruler and a protractor to draw a similar triangle.

       

    2. Measure the sides and altitude of your triangle and find its perimeter and area.
    3. Estimation Estimate the perimeter and area of the field.

C Challenge

Reasoning Complete each statement with always, sometimes, or never. Justify your answers.

48. Two similar rectangles with the same perimeter are _ ? _ modified under bar with  congruent.
49. Two rectangles with the same area are _ ? _ modified under bar with  similar.
50. Two rectangles with the same area and different perimeters are _ ? _ modified under bar with  similar.
51. Similar figures _ ? _ modified under bar with  have the same area.

Standardized Test Prep

SAT/ACT

GRIDDED RESPONSE

52. Two regular hexagons have sides in the ratio 3 : 5. The area of the smaller hexagon is 81   m 2 . 81 , m squared , .  In square meters, what is the area of the larger hexagon?

53. What is the value of x in the diagram below?

    

54. A trapezoid has base lengths of 9 in. and 4 in. and a height of 3 in. What is the area of the trapezoid in square inches?
55. In quadrilateral A B C D ,   m ∠ A = 62   , m ∠ B = 101   , eh b c d comma m angle . eh equals 62 comma . m angle . b equals 101 comma  and m ∠ C = 42   . m angle . c equals 42 .  What is m ∠ D ? m angle d question mark

Mixed Review

See Lesson 10-3.

Find the area of each regular polygon.

56. a square with a 5-cm radius
57. a pentagon with apothem 13.8 and side length 20
58. an octagon with apothem 12 and side length 10

See Lesson 7-5.

59. An angle bisector divides the opposite side of a triangle into segments 4 cm and 6 cm long. A second side of the triangle is 8 cm long. What are all possible lengths for the third side of the triangle?

Get Ready! To prepare for Lesson 10-5, do Exercises 60−62.

See Lesson 10-3.

Find the area of each regular polygon.

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