A triangular corner of a store has been roped off to be

46. Use the square configuration to complete the following

algebra rule: _________________________ NOTE: Simplify where possible. a + b 2 = b a a b a + b a + b 12 in. 5 in.

56. a Find a lower estimate of the area of the figure by

counting whole squares within the figure. b Find an upper estimate of the area of the figure by counting whole and partial squares within the figure. c Use the average of the results in parts a and b to provide a better estimate of the area of the figure. d Does intuition suggest that the area estimate of part c is the exact answer?

55. a Find a lower estimate of the area of the figure by

counting whole squares within the figure. b Find an upper estimate of the area of the figure by counting whole and partial squares within the figure. c Use the average of the results in parts a and b to provide a better estimate of the area of the figure. d Does intuition suggest that the area estimate of part c is the exact answer?

54. bisects of .

ST ⫽ 6 and TR ⫽ 9. If the area of is 25 m 2 , find the area of . 䉭SVT 䉭RST 䉭STR ∠STR TV

51. The area of a rectangle is 48 in

2 . Where x is the width and y is the length, express the perimeter P of the rectangle in terms only of x.

52. The perimeter of a rectangle is 32 cm. Where x is the

width and y is the length, express the area A of the rectangle in terms only of x.

53. Square DEFG is inscribed in

right as shown. If AD ⫽ 6 and EB ⫽ 8, find the area of square DEFG. 䉭ABC

50. In , AB ⫽

7 and BC ⫽12. The length of altitude to side is 5. Find the length of altitude from A to . DC AE BC AF ⵥABCD

49. In , QP ⫽

12 and QM ⫽9. The length of altitude to side is 6. Find the length of altitude from Q to . PN QS MN QR ⵥMNPQ

48. In the triangle whose sides are 13, 20, and 21 cm long, the

length of the altitude drawn to the 21-cm side is 12 cm. Find the lengths of the remaining altitudes of the triangle. In Exercises 47 to 50, use the fact that the area of the polygon is unique.

47. In the right triangle, find the length of the altitude drawn

to the hypotenuse. 20 cm 21 cm 13 cm 12 cm Q P N M R S A B F C D E A B D E G F C R T V S Perimeter of a Polygon Semiperimeter of a Triangle Heron’s Formula Brahmagupta’s Formula Area of Trapezoid, Rhombus, and Kite Areas of Similar Polygons Perimeter and Area of Polygons 8.2 KEY CONCEPTS TABLE 8.1 Perimeter of a Triangle Scalene Triangle Isosceles Triangle Equilateral Triangle Table 8.1 summarizes perimeter formulas for types of triangles, and Table 8.2 sum- marizes formulas for the perimeters of selected types of quadrilaterals. However, it is more important to understand the concept of perimeter than to memorize formulas. See whether you can explain each formula. We begin this section with a reminder of the meaning of perimeter. The perimeter of a polygon is the sum of the lengths of all sides of the polygon. DEFINITION a b c P = a + b + c b s s P = b + 2s s s s P = 3s TABLE 8.2 Perimeter of a Quadrilateral Quadrilateral Rectangle Square or Rhombus Parallelogram b d a c P = a ⫹ b ⫹ c ⫹ d h b b h P = 2b + 2h or P = 2b + h s s s s P = 4s b s s b P = 2b + 2s or P = 2b + s