The units of surface measure are obtained by squaring the units of linear measure.

Thus,

144122; 932; 30 = (51)2; 272 = (16)2

Ex. 105. (Oral.)

1. How many square feet of surface in a blackboard 4 ft. wide and 9 ft. long?

2. If a slate is 8 in. wide and has a surface of 80 sq. in., what is the length of the slate?

3. How many square inches in of a square foot? in &? in ? in ?

4. How many square feet in 3 sq. yds.? in 5 sq. yds.?

5. How many square inches in a board 4 in. long and 3 in. wide?

6. A square yard of carpet is 3 ft. long and 3 ft. wide; how many feet in it?

7. How many square feet in a yard of carpet 2 ft. wide? 2 ft. wide?

8. How many square feet in a room 12 ft. by 15 ft.?

9. How many yards of carpet 2 ft. wide will be required to cover the floor of the above room, if the strips run lengthwise of the room?

10. How many square yards in 81

sq. ft.?

11. How many square rods in of an acre?

12. What part of an acre are 40 sq. rds.? 80? 100 ?

Ex. 106.

1. Reduce 5 A. 147 sq.

rds. to

square rods.

2. How many square inches in 9 sq. yds. 7 sq. ft.?

3. Reduce 33,796 sq. in. to square yards.

4. Reduce 153 A. 87 sq. rds. to square inches.

5. In 67,413 sq. yds. how many acres?

6. In a rectangular field 49 yds. long and 16 yds. wide, how many square feet?

7. How many tiles 1 ft. square will be needed to pave a hall 20 ft. long and 9 ft. wide?

8. How much greater is the area of a lot 50 rds. square than that of a lot containing 50 sq. rds.?

9. How many square yards in a square lot measuring 142 ft. on a side?

10. Ingrain carpet is 3 ft. wide. be required for a room 27 ft.

How many yards will long and 18 ft. wide?

11. From each corner of a square, the side of which is 2 ft. 5 in., a square measuring 5 in. on a side is cut out. Find the area of the remainder of the figure.

12. Find the value of 0.45 of an acre.

13. Reduce of a square mile to lower denominations. rds. 2.42 sq. yds. to the decimal of an

14. Reduce 80 sq.

acre.

15. Add of an acre, sq. rd., and sq. yd. 16. Add of an acre and of a square rod. 17. From of a square rod take of a square yard. 18. Find of 9 A. 70 sq. rds. 15 sq. yds. 7 sq. ft. 19 sq. in. 19. A side of Russell Square in London is 660 ft. How many acres does it contain?

20. A garden 76 yds. long and 56 yds. broad, enclosed by a wall, has a border 4 ft. wide within the wall, and within this a path 5 ft. wide, the middle being grass. Find the areas of the border, path, and grass, respectively.

21. Subtract 18 A. 117 sq. rds. 17 sq. yds. from 367 A. 120 sq. rds.

22. What fraction of 223 sq. yds. 7 sq. ft. 120 sq. 31 sq. yds. 8 sq. ft. 120 sq. in. ?

in. are

23. How many planks, each 13 ft. long and 10 in. wide, will be required for the construction of a platform 54 yds. long and 21 yds. broad?

24. The area of a rectangular field is 33 sq. rds. 1 sq. yd. 6 sq. ft. 108 sq. in., and the length is 9 rds. 1 ft. 6 in. What is the width?

CARPETING ROOMS.

In determining the number of yards of carpeting required for a room, we first decide whether the strips shall run lengthwise or across the room, and then find the number of strips needed. The number of yards in a strip, including the waste in matching the pattern, multiplied by the number of strips will give the required number of yards.

25. How many yards of carpet 21 ft. wide will cover a floor 18 ft. long and 15 ft. wide, if the strips run across the room?

26. How many yards of carpeting of a yard wide will be required for a floor 26 ft. long, 15 ft. wide, if the strips run lengthwise. How many if the strips run across the room? How much will be turned under in each case?

27. How many yards of carpeting of a yard wide will be required for a room 8 yds. long and 17 ft. wide, if the strips run lengthwise and there is a waste of of a yard in each strip in matching patterns?

per

28. Find the cost of carpet 30 inches wide, at $1.25 yard, for a room 18 ft. by 14 ft., if the strips run lengthwise. If the strips run across the room.

29. Find the cost of carpeting of a yard wide, at $2.75 per yard, for a room 34 ft. 8 in. by 13 ft. 3 in., if the strips run lengthwise, and if there be a waste of of a yard on each strip in matching the pattern.

30. Which way must the strips of carpet of a yard wide run in order to carpet most economically a room 20 ft. 6 in. long and 19 ft. 6 in. wide, if there be no waste for matching the pattern?

PAPERING AND PLASTERING.

The area of the four walls of a room is equal to that of a rectangle whose length is equal to the circuit of the room, and whose breadth is equal to the height of the room.

31. How many yards of plastering in the four walls of a room 14 ft. 3 in. long, 13 ft. 4 in. wide, and 7 ft. high, if no allowance is made for doors and windows?

HINT. 14 ft. 3 in. 14 ft., and 13 ft. 4 in. = 133 ft.

32. Find the yards of plastering in the walls of a room 21 ft. long, 161 ft. wide, and 11 ft. high, if 12 sq. yds. be allowed for doors, windows, and baseboards?

33. How many square yards of plastering in the walls and ceiling of a room 30 ft. 8 in. long, 26 ft. 5 in. wide, 10 ft. 6 in. high, if 24 sq. yds. be allowed for doors, windows, and base-boards?

34. What will be the cost of plastering the walls and ceiling of a room 27 ft. 4 in. long, 20 ft. wide, and 12 ft. 6 in. high, at 27 cents per square yard, if 20 sq. yds. be deducted for doors, windows, and base-boards?

35. Find the cost of whitening the ceiling and walls of a room 14 ft. 4 in. wide, 15 ft. 6 in. long, and 10 ft. 6 in. high, at 5 cents per square yard, allowing 9 sq. yds. for doors and windows.

36. Find the cost of papering a room 32 ft. long, 22 ft.

wide, 13 ft. high, with paper 18 in. wide, 8 yds. in a roll, at $1.25 a roll, if 50 sq. yds. be allowed for doors, windows, and base-boards.