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11. Brick Requirement. Estimate the number of bricks needed for a wall 13 x 18 ft. having one door 4 ft x 9 ft and two windows each 3 ft x 6 ft. Each brick has faces measuring 8 x 2¹%, inches, with half-inch joints between bricks.

11. Brick Requirement. Estimate the number of bricks needed for a wall 13 x 18 ft. having one door 4 ft x 9 ft and two windows each 3 ft x 6 ft. Each brick has faces measuring 8 x 2¹%, inches, with half-inch joints between bricks.

Elementary Geometry For College Students, 7e
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.CT: Test
Problem 1CT
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** Example 15: An Application. The miter angle is the angle at which a saw or miter box must be set to cut a piece of stock to form a joint. It is equal to half the angle between the pieces to be joined. Find the miter angle for the pentagonal window in Fig. 6-59. Solution: The sum of the angles of the pentagon are, with n = 5. sam of angles = (-2)180° =(5-2)180-540 Each interior angle is then 540/5= 108. The miter angle is half of that, on 0=54° Exercise 3 Quadrilaterals 1. Find the area and perimeter of (a) a square of side 5.83 in. (b) a square of side 4.82 m. (c) a rectangle measuring 384 cm x 734 cm. (d) a rectangle measuring 55.4 in. by 73.5 in. 190 2. Find the area of (a) a parallelogram whose base is 4.52 ft and whose altitude is 2.95 ft. (b) a parallelogram whose base is 16.3 m and whose altitude is 22.6 m (c) a rhombus whose base is 14.2 cm and whose altitude is 11.6 cm (d) a rhombus whose base is 382 in, and whose altitude is 268 in. (e) a trapezoid whose bases are 3.83 m and 2.44 m and whose altitude is 1.86 m. (f) a trapezoid whose bases are 33.6 ft and 24.7 ft and whose altitude is 15.3 ft. Applications 3. What will be the cost, to the nearest dollar, of flagging a sidewalk 312 ft long and 6.5 ft wide, at $13.50 per square yard? 4. How many 9-in-square tiles will cover a floor 48 ft by 12 ft? 5. What will it cost to carpet a floor, 6.25 m by 7.18 m, at $7.75 per square meter? 6. How many rolls of paper, each 8.00 yd long and 18.0 in. wide, will paper the sides of a room 16.0 ft by 14.0 ft and 10.0 ft high, deducting 124 ft² for doors and windows? 3608 FIGURE 6-61 20.0 Chapter 6 Geometry 7. What is the cost of plastering the walls and ceiling of a room 40 ft long. 36 ft wide, and 22 ft high, at $8.50 per square yard, allowing 1375 ft² for doors, windows, and baseboard? 8. What will it cost to cement the floor of a cellar 25.3 ft long and 18.4 ft wide, at $3.50 per square foot? 720 9. Find the cost of lining a topless rectangular tank 68 in. long, 54 in. wide, and 48 in deep with zinc, weighing 5.2 lb per square foot, at $1.55 per pound installed. 10. A parcel of land lies between two parallel streets, Fig. 6-60. How many acres will remain in the parcel after the strip shown is taken for a new street? (1 acre- 43,560 ft²) 0 New Street FIGURE 6-58 75.0 FIGURE 6-59 845 Street /Street ( 350 f FIGURE 6-60 11. Brick Requirement. Estimate the number of bricks needed for a wall 13 x 18 f. having one door 4 ft Xx 9 ft and two windows each 3 ft x 6 ft. Each brick has faces measuring 8 x 2¹/4 inches, with half-inch joints between bricks. 12. Squares of Roofing Material. Roofing material is often specified in squares, where one square equals 100 ft². How many squares of shingles are needed to cover the roof of Fig. 6-61, neglecting waste? 13. Miter Angles: Calculate the miter angle for a (a) triangular window (equilateral) (b) square or rectangular frame (c) hexagonal window (d) octagonal wall clock 6-4 The Circle A circle, Fig. 6-62, is a plane curve in which all points are at a given distance (called the radius) from a fixed point (called the center). The diameter is twice the radius. The diameter cuts the circle into two semicircles. Circumference and Pi (#) The circumference of a circle is its total length, or the distance around. ■ Exploration: Try this. Wrap a strip of paper around a circular object, such as a jar lid, and mark the point where it starts to overlap. The length from the mark to the end of the strip
Transcribed Image Text:** Example 15: An Application. The miter angle is the angle at which a saw or miter box must be set to cut a piece of stock to form a joint. It is equal to half the angle between the pieces to be joined. Find the miter angle for the pentagonal window in Fig. 6-59. Solution: The sum of the angles of the pentagon are, with n = 5. sam of angles = (-2)180° =(5-2)180-540 Each interior angle is then 540/5= 108. The miter angle is half of that, on 0=54° Exercise 3 Quadrilaterals 1. Find the area and perimeter of (a) a square of side 5.83 in. (b) a square of side 4.82 m. (c) a rectangle measuring 384 cm x 734 cm. (d) a rectangle measuring 55.4 in. by 73.5 in. 190 2. Find the area of (a) a parallelogram whose base is 4.52 ft and whose altitude is 2.95 ft. (b) a parallelogram whose base is 16.3 m and whose altitude is 22.6 m (c) a rhombus whose base is 14.2 cm and whose altitude is 11.6 cm (d) a rhombus whose base is 382 in, and whose altitude is 268 in. (e) a trapezoid whose bases are 3.83 m and 2.44 m and whose altitude is 1.86 m. (f) a trapezoid whose bases are 33.6 ft and 24.7 ft and whose altitude is 15.3 ft. Applications 3. What will be the cost, to the nearest dollar, of flagging a sidewalk 312 ft long and 6.5 ft wide, at $13.50 per square yard? 4. How many 9-in-square tiles will cover a floor 48 ft by 12 ft? 5. What will it cost to carpet a floor, 6.25 m by 7.18 m, at $7.75 per square meter? 6. How many rolls of paper, each 8.00 yd long and 18.0 in. wide, will paper the sides of a room 16.0 ft by 14.0 ft and 10.0 ft high, deducting 124 ft² for doors and windows? 3608 FIGURE 6-61 20.0 Chapter 6 Geometry 7. What is the cost of plastering the walls and ceiling of a room 40 ft long. 36 ft wide, and 22 ft high, at $8.50 per square yard, allowing 1375 ft² for doors, windows, and baseboard? 8. What will it cost to cement the floor of a cellar 25.3 ft long and 18.4 ft wide, at $3.50 per square foot? 720 9. Find the cost of lining a topless rectangular tank 68 in. long, 54 in. wide, and 48 in deep with zinc, weighing 5.2 lb per square foot, at $1.55 per pound installed. 10. A parcel of land lies between two parallel streets, Fig. 6-60. How many acres will remain in the parcel after the strip shown is taken for a new street? (1 acre- 43,560 ft²) 0 New Street FIGURE 6-58 75.0 FIGURE 6-59 845 Street /Street ( 350 f FIGURE 6-60 11. Brick Requirement. Estimate the number of bricks needed for a wall 13 x 18 f. having one door 4 ft Xx 9 ft and two windows each 3 ft x 6 ft. Each brick has faces measuring 8 x 2¹/4 inches, with half-inch joints between bricks. 12. Squares of Roofing Material. Roofing material is often specified in squares, where one square equals 100 ft². How many squares of shingles are needed to cover the roof of Fig. 6-61, neglecting waste? 13. Miter Angles: Calculate the miter angle for a (a) triangular window (equilateral) (b) square or rectangular frame (c) hexagonal window (d) octagonal wall clock 6-4 The Circle A circle, Fig. 6-62, is a plane curve in which all points are at a given distance (called the radius) from a fixed point (called the center). The diameter is twice the radius. The diameter cuts the circle into two semicircles. Circumference and Pi (#) The circumference of a circle is its total length, or the distance around. ■ Exploration: Try this. Wrap a strip of paper around a circular object, such as a jar lid, and mark the point where it starts to overlap. The length from the mark to the end of the strip
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