9.3 EXERCISES. 2. A square with area 16 square cm has perimeter cm.

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1 9. EXERISES Fill in each blank with the correct response. 1. The perimeter of an equilateral triangle with side length equal to inches is the same as the perimeter of a rectangle with length 10 inches and width 8 inches.. If the area of a certain triangle is 4 square inches, and the base measures 8 inches, then the height must measure inches. 5. The area of an equilateral triangle with side length 6 inches is square inches.. square with area 16 square cm has perimeter cm. 4. If the radius of a circle is doubled, then its area is multiplied by a factor of. 6. If the length and the width of a rectangle are doubled, then the area is multiplied by a factor of.

2 9. Perimeter, rea, and ircumference 519 Use the formulas of this section to find the area of each figure. In Eercises 19, use.14 as an approimation for cm 1_ cm 4 cm cm in. 1_ in. 1.5 cm 4 in. (a parallelogram) 4 in. (a parallelogram) (a parallelogram) 6 mm 8 mm m 5 m 5 mm mm 17. b = 18. b = 4 cm 19. h = cm = 5 cm (a trapezoid) h = = 5 cm (a trapezoid) 1 cm cm 6 m 1 m Solve each of the following problems.. Window Side Length stained-glass window in a church is in the shape of a square. The perimeter of the square is 7 times the length of a side in meters, decreased by 1. Find the length of a side of the window. 4. imensions of a Rectangle video rental establishment displayed a rectangular cardboard stand-up advertisement for the movie Sweet Home labama. The length was 0 in. more than the width, and the perimeter was 176 in. What were the dimensions of the rectangle? 5. imensions of a Lot lot is in the shape of a triangle. ne side is 100 ft longer than the shortest side, while the third side is 00 ft longer than the shortest side. The perimeter of the lot is 100 ft. Find the lengths of the sides of the lot.

3 50 HPTER 9 Geometry 6. Pennant Side Lengths wall pennant is in the shape of an isosceles triangle. Each of the two equal sides measures 18 in. more than the third side, and the perimeter of the triangle is 54 in. What are the lengths of the sides of the pennant? 7. Radius of a ircular Foundation The Peachtree Plaza Hotel in tlanta is in the shape of a cylinder, with a circular foundation. The circumference of the foundation is 6 times the radius, increased by 1.88 ft. Find the radius of the circular foundation. (Use.14 as an approimation for.) 8. Radius of a ircle If the radius of a certain circle is tripled, with 8. cm then added, the result is the circumference of the circle. Find the radius of the circle. (Use.14 as an approimation for.) 9. rea of Two Lots The survey plat in the figure shows two lots that form a trapezoid. The measures of the parallel sides are ft and ft. The height of the trapezoid is ft. Find the combined area of the two lots. Round your answer to the nearest hundredth of a square foot. 0. rea of a Lot Lot in the figure is in the shape of a trapezoid. The parallel sides measure 6.84 ft and 8.05 ft. The height of the trapezoid is ft. Find the area of Lot. Round your answer to the nearest hundredth of a square foot. 1. Perimeter or rea? In order to purchase fencing to go around a rectangular yard, would you need to use perimeter or area to decide how much to buy?. Perimeter or rea? In order to purchase fertilizer for the lawn of a yard, would you need to use perimeter or area to decide how much to buy? In the chart below, one of the values r (radius), d (diameter), (circumference), or (area) is given for a particular circle. Find the remaining three values. Leave in your answers.. 4. r d 6 in. 9 in ' 8.05' S 8 4' E 175.4' W/F LG. N PIERS LT S 78 58' W ' 6.84' 88.96' ' ft 40 ft 1 18 cm cm N 11 17' W 88.95' W/F LG. N PIERS LT ' TIN LG. S 10 6' E in. in. S 78 58' W ' Property survey of lot in New Roads, Louisiana. Each of the following figures has perimeter as indicated. (Figures are not necessarily to scale.) Find the value of. 41. P P 4 4. P P

4 9. Perimeter, rea, and ircumference 51 Each of the following figures has area as indicated. Find the value of Each of the following circles has circumference or area as indicated. Find the value of. Use.14 as an approimation for (a trapezoid) 5 (e) The rectangle in part (b) had sides twice as long as the sides of the rectangle in part (a). ivide the larger area by the smaller. y doubling the sides, the area increased times. (f) To get the rectangle in part (c), each side of the rectangle in part (a) was multiplied by. This made the larger area times the size of the smaller area. (g) To get the rectangle of part (d), each side of the rectangle of part (a) was multiplied by. This made the area increase to times what it was originally. (h) In general, if the length of each side of a rectangle is multiplied by n, the area is multiplied by. Job ost Use the results of Eercise 5 to solve each of the following. 54. ceiling measuring 9 ft by 15 ft can be painted for $60. How much would it cost to paint a ceiling 18 ft by 0 ft? 55. Suppose carpet for a 10 ft by 1 ft room costs $00. Find the cost to carpet a room 0 ft by 4 ft. 56. carpet cleaner charges $80 to do an area 1 ft by 1 ft. What would be the charge for an area 9 ft by 9 ft? 57. Use the logic of Eercise 5 to answer the following: If the radius of a circle is multiplied by n, then the area of the circle is multiplied by. 58. Use the logic of Eercise 5 to answer the following: If the height of a triangle is multiplied by n and the base length remains the same, then the area of the triangle is multiplied by Work through the parts of this eercise in order, and use it to make a generalization concerning areas of rectangles. (a) Find the area of a rectangle 4 cm by 5 cm. (b) Find the area of a rectangle 8 cm by 10 cm. (c) Find the area of a rectangle 1 cm by 15 cm. (d) Find the area of a rectangle 16 cm by 0 cm. 4 Total rea as the Sum of reas y considering total area as the sum of the areas of all of its parts, the area of a figure such as those in Eercises 59 6 can be determined. Find the total area of each figure. Use.14 as an approimation for in Eercises 61 and (a parallelogram and a triangle) (a triangle, a rectangle, and a parallelogram)

5 5 HPTER 9 Geometry rea of a Shaded Portion of a Plane Figure The shaded areas of the figures in Eercises 6 68 may be found by subtracting the area of the unshaded portion from the total area of the figure. Use this approach to find the area of the shaded portion. Use.14 as an approimation for in Eercises 66 68, and round to the nearest hundredth cm 18 ft (a rectangle and two semicircles) cm 48 cm cm 7 ft 1 ft (a triangle within a trapezoid) 11 ft 74 cm 16 cm 4 cm 1 ft (a square and four semicircles) 19 cm 8 cm (a triangle within a trapezoid) ft 70. heese pizza with two toppings: 10-in. pizza sells for $7.99, 1-in. pizza sells for $9.99, 14-in. pizza sells for $ ll Feasts pizza: 10-in. pizza sells for $9.99, 1-in. pizza sells for $11.99, 14-in. pizza sells for $ Etravaganza pizza: 10-in. pizza sells for $11.99, 1-in. pizza sells for $1.99, 14-in. pizza sells for $ polygon can be inscribed within a circle or circumscribed about a circle. In the figure, triangle is inscribed within the circle, while square WXYZ is circumscribed about it. These ideas will be used in some of the remaining eercises in this section and later in this chapter. W Z Eercises 7 80 require some ingenuity, but all may be solved using the concepts presented so far in this chapter. 7. iameter of a ircle Given the circle with center and rectangle, find the diameter of the circle. X Y (two congruent triangles within a rectangle) (a semicircle within a rectangle) 4 cm 6 m = 1 in. = in. (a circle within a square) (two circles within a circle) Pizza Pricing The following eercises show prices actually charged by Maw-Maw Gigi s, a local pizzeria. In each case, the dimension is the diameter of the pizza. Find the best buy. 69. heese pizza: 10-in. pizza sells for $5.99, 1-in. pizza sells for $7.99, 14-in. pizza sells for $ Perimeter of a Triangle What is the perimeter of E, if 0 in., 0 in., and 4 in.? F E

6 9.4 The Geometry of Triangles: ongruence, Similarity, and the Pythagorean Theorem rea of a Square The area of square PQRS is 150 square feet. T, U, V, and W are the midpoints of PQ, QR, RS, and SP, respectively. What is the area of square TUVW? 78. Perimeter of a Polygon an the perimeter of the polygon shown be determined from the given information? If so, what is the perimeter? P T Q 7 in. W S V U R 1 in. 79. rea of a Shaded Region Epress the area of the shaded region in terms of r, given that the circle is inscribed in the square. 76. rea of a Quadrilateral The rectangle has length twice the width. If P, Q, R, and S are the midpoints of the sides, and the perimeter of is 96 in., what is the area of quadrilateral PQRS? r P S 77. rea of a Shaded Region If is a square with each side measuring 6 in., what is the area of the shaded region? E R Q 80. rea of a Trapezoid Find the area of trapezoid, given that the area of right triangle E is 0 in.. 6 in. E = 14 in. 9.4