The area of a surface is expressed by the product of the two numbers representing the two dimensions.

106. A Rectangle is a figure having four sides, each of which is perpendicular to two of the other sides.

A slate, a book and a sheet of paper are examples of rectangles.

107. A Square is a rectangle whose four sides are equal. A square inch is a square whose sides are each one inch long. The unit of measure in surface measure is a square whose length is known, as an inch or a foot.

A

D

B

C

In the rectangle A B C D, five feet long and three feet wide, the unit of measurement is the square foot, and the area is equal to the number of units contained in the rectangle, which is found by actual count to

be 15, or 5×3. From this and similar processes we derive the

RULE.

To find the area of a rectangle, multiply the length by the breadth; the product is the area.

TABLE.

144 square inches (sq. in.) = 1 square foot,

sq. ft. sq. yd.

= 1 square rod or perch, rd. or P.

1 acre

1 square mile,

A.

sq. mi.

The rood, now but seldom used, is equal to 40 square rods.

COMPARISON OF UNITS.

1 A. 160 sq. rd. = 4840 sq. yd. = 43560 sq. ft. = 6272640 sq.

=

=

in.

in.

1 sq. rd. 304 sq. yd.

ORAL EXERCISE.

1. How many sq. in. in 3 sq. ft.? In 1 sq. yd.?

2. How many sq. ft. in 6 sq. yd.? In 288 sq. in.? 3. How many sq. yd. in 10 sq. rd.? In 81 sq. ft.? 4. How many rods in 10 A.? In A.? In & A.? 5. At 10 cts. a sq. ft. how much will 1 A. cost?

WRITTEN PROBLEMS.

1. Reduce 871200 sq. ft. to acres.

Ans. 20 A.

2. How many acres in a township 6 miles square?

Ans. 23040.

3. A rectangular piece of land is 40 rd. long and 12 rd. wide: how many acres does it contain?

Ans. 3. 4. A rectangular piece of land is 14 rd. 6 ft. long and 12 rd. 3 ft. wide: how many acres does it contain?

Ans. 1 A. 14 sq. rd. 29 sq. yd. 4 sq. ft. 72 sq. in. 5. Bought 12 acres of land at $200 an acre, and sold it at Ans. $39417.60.

8 cts. a sq. ft. what was the gain?

6. What part of an acre is a town-lot 60 ft. by 160 ft?

Ans. 80

8. 363

7. What part of an acre is a town-lot 25 ft. by 120 ft?

Ans. 25

MEASURES OF VOLUME.

25.

363

108. Cubic Measure is used in computing the contents of volumes or solids.

109. A Volume or Solid has three dimensions-length, breadth and thickness.

The volume of a body is expressed by the product of the numbers representing its three dimensions.

110. A Cube is a volume bounded by six equal squares, which are called its faces. The three dimensions of a cube are equal.

A cubic inch is a cube each side of which is one inch in length.

TABLE.

1728 cubic inches (cu. in.) = 1 cubic foot, cu. ft.

27 cubic feet

- 1 cubic yard, cu. yd.

1. How many cu. ft. in 2 cu. yd.? In 5 cu. yd.?

2. How many cu. ft. in 3 cords? In 5 cords? In cord?

3. How many cu. ft. in 2 pch. of stone? In 6 pch.?

4. How many cords in 256 cu. ft.? In 26 cd. ft.?

WRITTEN PROBLEMS.

1. How many cu. ft. in 16 pch. of stone?

2. In a 13-inch cube how many cu. in.? 3. In of a cd. how many cu. ft.?

Ans. 396.

Ans. 2197.

Ans. 96.

4. In a pile of wood 20 ft. long, 4 ft. wide and 6 ft. high, how many cords?

Ans. 33.

5. What is the difference between a 6-inch cube and 6 cu. in. ? Ans. 210 cu. in.

6. How many cu. ft. in a block 6 ft. long, 4 ft. wide and 3 ft. high? Ans. 72 cu. ft.

7. How many 2-foot cubes could be cut from a block 6 ft. high, 8 ft. long and 4 ft. wide?

Ans. 24.

8. How many perch of stone in a wall 20 ft. long, 6 ft. high and 3 ft. wide? Ans. 14.

MEASURES OF CAPACITY.

111. Measures of Capacity are used to determine the quantity of fluids and of many dry substances.

They are therefore of two kinds-Measures of Liquids and Measures of Dry Substances.

The unit of Liquid Measure is the gallon, and of Dry Measure the bushel.

The ale gallon contains 282 cu. in., but is now rarely used. The barrel and the hogshead are no longer fixed measures, but vary, and their contents are estimated by gallons. In estimating the capacity of cisterns, reservoirs, etc., 1 barrel (bbl.) = 31 gallons.

1 hogshead (hhd.) = 63 gallons.

ORAL EXERCISE.

1. How many gills in 6 pt.? In 2 qt.? 2. How many pints in 20 gi.? In 6 gal.? 3. How many quarts in 40 gal.? In 200 gi.? 4. If a gill of wine cost 5 cents, how much will a gallon cost?

5. How many pints in 6 gal. 3 qt.?

6. If 1 gal. of oil cost 80 cents, how much will 5 gal. and 1 pt. cost?

7. How many five-gallon kegs can be filled from a hogshead of 63 gal.?

DRY MEASURE.

113. Dry Measure is used in measuring grain, fruit, salt, soft coal, etc.

The Winchester bushel, which is the unit of measure, contains 2150.42 cubic inches.

1 pint dry measure = nearly 14 pt. liquid measure.

In measuring small seeds, beans, grain, etc. the measure must be even full. Four heaped measures are equal to five

even measures.

A heaped bushel equals 2688 cu. in., or § of an even bushel.

ORAL EXERCISE.

1. How many pints in 7 pk.? In 3 bu.?

2. How many pints in 1 bu. 3 pk.?

3. How many quarts in 3 bu. 3 pk.?

4. How many pecks in 27 pt.? In 18 qt.? 5. How many pints in 3 bu. 3 pk. 3 qt.?

WRITTEN PROBLEMS.

1. How many pints in 6 gal. 1 qt. 1 pt.?

2. How many pints in 18 bu. 3 pk.?

3. How many bushels in 17632 pt. of beans?

Ans. 51.

Ans. 1200.

Ans. 2751.

4. What is the difference between a quart of wine and a

quart of clover-seed in cubic inches?

Ans. 9.45 cu. in.

5. Bought 5 bushels of chestnuts at $4 a bushel, and sold them at 15 cents a quart: how much was the gain?

Ans. $4.