C Challenge

42. Algebra One base of a trapezoid is twice the other. The height is the average of the two bases. The area is 324   cm 2 . 324 , cm squared , .  Find the height and the bases. (Hint: Let the smaller base be x.)

43. Sports Ty wants to paint one side of the skateboarding ramp he built. The ramp is 4 m wide. Its surface is modeled by the equation y = 0 . 25 x 2 . y equals . 0 . 25 , x squared , .  Use the trapezoids and triangles shown to estimate the area to be painted.

    
    Image Long Description

44. In trapezoid ABCD below, A B ¯ || D C ¯ . eh b bar , vertical linevertical line , d c bar , .  Find the area of ABCD.

    

Standardized Test Prep

SAT/ACT

45. The area of a kite is 120   cm 2 . 120 , cm squared , .  The length of one diagonal is 20 cm. What is the length of the other diagonal?
    1. 12  cm 12 , cm
    2. 20  cm 20 , cm
    3. 24  cm 24 , cm
    4. 48  cm 48 , cm
46. Δ A B C ∼ Δ X Y Z . A B = 6   , B C = 3   , cap delta eh b c tilde operator cap delta x y z . eh b equals 6 comma b c . equals 3 comma  and C A   = 7   . c eh equals 7 .  Which of the following are NOT possible dimensions of Δ X Y Z ? cap delta x y z question mark
    6. X Y = 3   , Y Z = 1   . 5 , Z X = 3   . 5 x y equals 3 comma . y z equals 1 . 5 comma . z x equals 3 . 5
    7. X Y = 9   , Y Z = 4   . 5 , Z X = 10   . 5 x y equals 9 comma . y z equals 4 . 5 comma . z x equals 10 . 5
    8. X Y = 10   , Y Z = 7   , Z X = 11 x y equals 10 comma . y z equals 7 comma . z x equals 11
    9. X Y = 18   , Y Z = 9   , Z X = 21 x y equals 18 comma . y z equals 9 comma . z x equals 21

Short Response

47. Draw an angle. Construct a congruent angle and its bisector.

Mixed Review

See Lesson 10-1.

48. Find the area of a right isosceles triangle that has one leg of length 12 cm.

49. A right isosceles triangle has area 112 . 5   ft 2 . 112 . 5 , ft squared , .  Find the length of each leg.

50. Find the measure of an interior angle of a regular nonagon.

See Lesson 6-1.

Get Ready! To prepare for Lesson 10-3, do Exercises 51–53.

See Lesson 8-2.

Find the area of each regular polygon. Leave radicals in simplest form.

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