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5. The Area of a surface is the number of square units it contains.

1

2

3

The area of the rectangle A. B. is 12 4 5 6

squares; they may be square inches, square

feet, or square rods, etc. 9

Since there are 4 rows of 3 squares each,

12 squares, is denoted by the product 10 11 12

of 4 by 3; i.e., by the product of the length

by the breadth. B

If by 4, four squares are meant, is 3 to be considered an abstract or a denominate number?

the area,

FORMULA (Indicated Process). Area of rectangle Length x Breadth.

NOTE. —The rule implies that the length and breadth are expressed in the same denomination.

Common Square Measure.

Table.
144 Square Inches (sq. in.) 1 Square Foot (sq. ft.).
9 Square Feet

1 Square Yard (sq. yd.).
s i Square Rod (sq. rd.).

1 304 Square Yards

1 Perch. 160 Square Rods

1 Acre (A.).
640 Acres

1 Square Mile (sq. mi.).
1 Section of Land.

{ ={

sq. mi. A

sq. rd.

sq. in.

=

8q. ft.
1=- 640 = 102,400 = 27,878,400 4,014,489,600.

Scale : 144, 9, 30ḥ, 160, 640.
NOTE.—40 Perches 1 Rood (R.); 4 Roods=1 Acre.

Units.

The unit for land is the acre ; for plastering, ceiling, etc., it is the sq. yd. ; for paving, glazing, and stone-cutting, it is the sq. ft.; for roofing, flooring, and slating, it is a square 10 ft. by 10 ft., or 100 sq. ft.

Surveyors' Square Measure.

Table.

625 Square Links (sq. 1.) : 1 Sq. Rd., or Percb (P.).
16 Square Rods

1 Sq. Chain.
10 Square Chains

1 Acre. 640 Acres

1 Sq. Mile. 36 Sq. Miles

= 1 Township (Tp.).

EXERCISES.
Reduce :

1. 54 A. 10 P. to perches (sq. rd.).
2. 624 P. to sq. yds.
3. 5 A. 145 P. to sq. ft.
4. 250 P. 17 sq. yd. to sq. inches.
5. 2 A. 70 P. 30 sq. yd. to sq. inches.
6. 10 sq. yd. 4 sq. ft. 15 sq. in, to sq. inches.
7. 3,737,796 sq. ft. to acres, etc.
8. 3 A. 37 sq. rd. 5 sq. yd. 7 sq. ft. to sq. inches.

.
9. 295,376 sq. in. to units of higher denominations.
10. 31 sq. mi. 48 A. to sq. ch.
11. 2,000,000 sq. 1. to acres.
12. 10,800 sq. ch. to sq. miles.
13. f of A. to sq. inches.

.

Process.

7

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160

Х 1

121 4

30 = 141

Х

x x 144 = 4,878,720 sq. 9

. in. 14. [ of A. to units of lower denominations.

g

1

Process.

[ocr errors]

f A.=] of 160 sq. rd. 1244 sq. rd.

sq. rd. = of 141 sq. yd. 134 sq. yd.
$sq. yd. =
of 9 sq. ft. =4 sq. ft.

.
Hence į A. 124

yd. 4

[ocr errors]

sq.
rd. 13

sq.

ft.

sq.

15. A. to units of lower denominations.
16. sq. rd. to lower denominations.
17. A. to sq. chains.
18. section of land to sq. 1.
19. 25,373,896 sq. 1. to higher denominations.
20. 8 chains to sq. rods.
21. 1 sq. mi. 4 sq. ch. 53 sq. 1. to links.
22. 47,916 sq. ft. to higher denominations.
23. 871,200 sq. ft. to acres.
24. 89,794,172 sq. in. to acres, etc.
25. 20,000 sq. ft. to sq. rods.

PROBLEMS.

Indicate the process first, and abridge the work by cancellation.

1. A rectangular piece of land is 40 rd. long and 12 rd. wide. Find the acres in it.

2. A floor is 8 ft. by 16 ft. How many sq. ft. in it?
3. A ceiling is 17 ft. by 20 ft. How many sq. yds. in it?
4. The side of a square is 6 feet. Find its area.
5. A table is 6 ft. by 2 ft. Find its area in sq. in. .
6. A garden is 656 ft. by 93 ft. Find the sq. rd. in it.

7. A fence surrounding a mile race-course is 6 ft. high. How many sq. yd. in it? Find the cost at 10 cents a sq. yd.

8. A room is 20 by 30 feet. How much will it cost to carpet the room with carpet 1 yd. wide at $1.00 per yd.?

9. A field contains 12 acres and is 24 rds. wide. Find its length.

10. I bought 10 acres of land at $200 an acre and sold it at 8 cts. a sq. ft. Find the gain.

11. Find the cost of a piece of oil-cloth 25 feet long and 16 feet 9 inches wide, at 95 cents a square yard.

12. What will it cost to carpet a room 18 feet long and 25% feet wide at $1.25 a yard, the carpet being å yd. wide ?

13. A school-room measures as follows: Length, 72 ft.; width, 22; ft.; height, 16 ft. Deduct 245 sq. ft. for doors and windows, and find the cost of plastering at 16) cts. per

sq. yd.

14. Show the difference between 6 sq. ft. and 6 feet square.

15. A room is to be plastered and painted; its length is 20 ft., its width 18 ft., its height 12 feet; the rate will be 33} cts. per sq. yd. Find the cost of the work.

16. Find the value of a field 180 rd. long and 943 rd. wide at $18 an acre.

17. How many yds. of carpeting, 3 ft. 6 in. wide, will it take to cover a floor 21 ft. wide and 36 ft. long, the carpet running lengthwise ?

18. A room measures 18 ft. X 15 ft. X 10 ft. Find the cost of papering it with paper 24 in. wide at $.85 a roll, 8 yd. in a roll, making a deduction of 20 sq. yd. for openings.

19. A sidewalk is 10 ft. wide, exclusive of the curb, and is 100 ft. long. How many 4 X 8 bricks in it?

20. A 15 by 18 ft. room is to be carpeted. Which will be the cheaper way to run yard-wide strips, lengthwise or breadth wise?

21. A room is 18 ft. wide and 9 ft. high. After deducting from the area of one end two windows 6 ft. X 41 ft., find the number of sq. yd. remaining to be plastered.

22. A rectangular piece of land 1320 yds. long and 2 rods wide was taken for public use. How much was due the owner at $160 an acre ?

23. A barn is roofed with shingles put 6 in. to the weather. Find the cost at $12 per M. if the roof is 60 feet long, each side being 32 feet, the first course along the eaves being doubled. [1000 shingles to 110 sq. feet.]

24. Find the cost of slating a roof 64 ft. 9 in. long and 45 ft. wide at $15.371 per square.

25. How many bricks will pave a sidewalk 25 ft. by 10 ft., a brick measuring 8 in. X 4 in. X 2 in.?

26. How many bricks, set on end, will pave a sidewalk containing one-half the last area ?

MEASURES OF VOLUME.

1. A Solid has length, breadth, and thickness.

2. A Rectangular Solid is bounded by six rectangular faces.

a

3. A Cube has six equal faces and twelve equal edges.

4. Volume, or Solid Contents, of a body is the number of cubic units it contains.

5. If on a rectangle of 12 sq. ft., as a base, we erect a rectangular solid 5 feet high, the structure will contain 3 times

4, or 12, cubic feet for each of the 5 feet of height. Hence, the volume of the solid will be 5 times 12, or 60, cubic feet.

RULE.

The volume of a rectangular solid is the number of cubic units denoted by the product of its length, breadth, and thickness.

NOTE.-The rule implies that the three dimensions are all of the same denomination.

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