54. How many square yards of oil-cloth are needed to cover a floor 18 ft. by 24 ft. 6 in. ?

He

55. A owns a city lot 168 ft. long and 42 ft. wide. uses of it for a lawn. How many square yards does the

lawn contain?

56. How long will it take a man to mow the above lot, if it takes him a minute to run a 2-foot lawn-mower lengthwise of the lot?

57. A pony can reach 40 feet in any direction from the stake to which he is picketed. Over how many square rods of surface can he graze?

58. What is the diameter of a tree that is 10 feet in circumference?

59. A basin measures 9 inches across the top and 6 inches across the bottom. How much farther around the top than around the bottom?

60. How many acres of land are enclosed by a circular mile track?

61. A landscape gardener lays off a circular grass-plot whose radius is one rod, and near it a semicircular plot having a radius two rods in length. Compare their areas.

62. If the area of a triangle is 9 acres and the base is 80 rods, what is the altitude?

63. Find the area of one gable end of a building 40 ft. wide, the ridge being 15 ft. above the eaves.

64. Find area of a triangle whose altitude is 14 ft. and its base 12 ft.

65. Find the area of triangle whose altitude is 4 in. and base 12 in.

CARPETING ROOMS.

175. In making a carpet, the carpeting is cut from a roll into strips which are usually laid from end to end of the floor, or lengthwise. Sometimes the strips are laid

across the room.

1. How much carpeting must I purchase to cover a room 6 yd. long and 43 yd. wide, strips running lengthwise?

SOLUTION. It will be necessary to purchase as much carpeting as if the room were 5 yd. wide, the excess of under in the last strip.

1 strip contains 6 yd. 5 strips 5 times 6 yd.

2. How many yards must I purchase, if the strips are laid across the room?

SOLUTION. - 1 strip contains 4 yd. 6 strips

6 times 4 yd.

434 yd.

yd. being turned

carpeting to cover a room, on account of the waste in matching patterns.

This diagram represents the floor in Ex. 1. in which the strips are laid lengthwise. Pupils should draw a similar diagram for each floor.

NOTE. Carpeting is sold by lineal yards or meters, not by

square measure.

3. A merchant bought a roll of carpet containing 74 yd. at 85 a yard, and sold it at $1.15 a yard. What was his profit ?

4. A roll of carpet

yd. wide contains 60 yards; how

many square yards of surface will it cover?

5. How many strips of carpet 3 ft. wide will cover a floor 15 ft. wide? 17 ft wide? 18 ft. wide?

6. How many strips 27 in. wide are required for a floor 12 ft. wide? 14 ft. wide? 16 ft. wide ?

7. If, in Example 5, the room is 16 ft. long, how many linear yards of carpet will be needed to cover the floor?

8. If, in Example 6, the room is 19 ft. long, how many yards will be required to cover the floor?

9. How many yards of ingrain carpet 2 yd. wide will be required for a floor 17 ft. wide and 20 ft. long, strips running across the room?

10. How much will a carpet cost at $.90 a yard to cover a floor 22 ft. long and 15 ft. wide, if the strips run crosswise, and no allowance is made for matching?

11. How many yards of carpet yd. wide will be required for a floor 20 ft. long and 15 ft. wide, if the strips run across the room?

12. How many yards of carpet 1 yd. wide will be required for a floor 18 ft. long and 14 ft. wide, strips running across the room?

13. How many yards of carpeting are needed to cover a floor 24 ft. long and 17 ft. wide, strips running lengthwise and yd. wide?

14. If my room is 16 ft. long and 12 ft. wide, how many yards of carpeting 24 inches wide must I buy, if in cutting 6 inches is allowed on each strip for matching?

15. I wish to have a carpet woven. My room is 21 ft. long and 17 ft. wide; how much carpeting, 34 inches wide, must I order to exactly cover the room, no allowance being made for matching?

16. How many yards of carpet 2 ft. wide will cover a floor 7 yards long and 14 ft. wide, if strips run lengthwise, and it requires yd. for matching?

17. What will it cost to carpet a room 15 ft. by 17 ft., with carpet 30 inches wide, at $1.20 per lineal yard, if the strips run lengthwise, and an allowance of 9 in. to each strip be made for matching?

18. How much less would be the cost with no loss for matching?

19. A room 31 ft. by 17 ft. is to be covered with carpeting 30 in. wide. How many yards must be purchased, and how wide a strip must be turned under?

20. At $2.50 a yard, what will be the cost of a carpet to cover a parlor floor 6 yd. long and 54 yd. wide, if 3 yd. is wasted in matching?

21. How many yards of matting 1 yd. wide will be required for an assembly room 85 ft. 8 in. long and 64 ft. 6 in. wide, strips running across the room?

22. A room 17 ft. 6 in. long, 14 ft. wide, is to be carpeted with carpet yd. wide. A border 3 yd. wide goes around the outside. How many yards of border, and how many yards of carpet if strips run lengthwise, and there is a waste of one foot on each strip for matching?

PLASTERING AND PAINTING, ETC.

176. Plastering and Painting are usually done by the square yard. Allowance is sometimes made for doors and windows, which are called openings. Allowance is also sometimes made for base-boards and wainscoting.

1. A room is 18 ft. long, 12 ft. wide, and 10 ft. high. How many square yards in the walls and ceiling, making no allowance for openings?

NOTE. Let the pupils draw a diagram for each room, representing the four walls in a line. The entire

2. Find the cost of plastering the walls and ceiling of a room 35 ft. long, 26 ft. 6 in. wide, and 15 feet high, at $.45 a sq. yd., allowing 1024 sq. ft. for doors, windows, and base-board.

3. How many square yards of plaster in the sides and ceiling of a room 30 ft. long, 24 ft. wide, and 10 ft. high, allowing for a base-board 1 ft. high, 2 doors 3 ft. by 8 ft., and 4 windows 3 ft. by 6 ft.?

4. Find the cost of plastering the ceiling of a room 18 ft. by 20 ft., at 10 cents a square yard.

5. A room 15 ft. by 18 ft., and 10 ft. high, has 4 doors each 3 ft. by 7 ft., and three windows each 3 ft. by 6 ft. Find the cost of plastering the walls and ceiling of the room at 30 cents a square yard, deducting one-half the surface for openings.

6. How many sq. yds. of plastering in the ceiling of a room 20 ft. long, 9 ft. high, and 15 ft. wide, no allowance for openings?

7. At $.30 a sq. yd., how much will it cost to plaster a room 21 ft. 6 in. long, 16 ft. wide, and 9 ft. high, the base-board being 8 inches wide, and allowing for 3 windows