Q. What are your ideas of a square? A. It is A any thing which is as long as it is wide. Q. What kind of a figure does this on the right appear to be? A. A square figure.

Q. Why? A. Because the side AB is as long as the side BC.

Q. How many sides has this figure, and what is their length?

Q. How many equal corners has it? A. Four. Q. What are these corners generally called? A. Angles.

Q. How, then, would you describe a square figure? equal sides, and four equal angles.

A. It has fo

Q In the above figure, if each side be 1 foot in length, what ought it te bá called? A. I square foot.

Q. If the sides of a square be each 1 yard in length, as in the figure on the right, what ought it to be called? A. 1 square yard.

Q. In this square I perceive there are several smaller squares, contained in the larger. If you count all the smaller squares, allowing each one to be 1 foot, how many square feet or square yards will they make?

Q. Why? A. Because there are 9 small squares, each containing 1 square foot, which make 9 square feet, that is, 1 square yard.

3 feet 1 yard

A 3 feet1 yard. B

D

Q. How many square feet, then, make 1 square yard? A. 9.

Q. If we multiply 3 feet (the length of I side) by the width, 3 feet, making 9, the same result is produced as before. What, then, will multiplying the A. The length of any square by the breadth, or the length into itself, give? square feet, square inches, &c., contained in the figure.

Q. How many square inches in a figure 2 inches long and 2 inches wide: 2 x 2=4, Ans. How many in a figure 4 inches long and 4 inches wide? 12 inches square, that is, 12inches long, and 12 inches wide? 8 inches square 6 inches square? 20 inches square? 30 inches square?

Q How many square feet in a figure 1 foot, or 12 inches, square?

square fool.

Q. How many square inches in 1 square foot? and why? A. 144. because 12 in. x 12 in. 144.

Ꭿ. ]

Sq in.

Q. How many square feet in 1 square yard? and why? A. Y sq. A.· Decause 3 ft. x 3ft

2. How many equare yards in 1 square roa? ona why? A. 303 sq, yds. because 5 vs. X 54 yds.= = =301

Q. How many square feet in 1 square rod? and why? A. 2721 sq. ft. · because 16 ft. (the number of feet in 1 rod in length) × 164 it =2724

A

Q. This figure on the right is called a parallelogram: what, then, are your ideas of a parallelogram? A. That it is a figure, which is longer than it is wide. F

D

B

E

Q. We see by this figure, that there are two kinds of parallelograms, viz ABCD and ABEF. By inspecting these they will oe found to be equal: how, then, may a parallelogram be defined? A. It is a figure which has its opposite sides of equal length, and its opposite angles equal.

Q. If this figure had been square, and each side 2 feet in length. it is plain that it would have contained 4 square feet; but, allowing the longest side to be 2 fect, and the shortest side only foot, it will, of course, contain but as many A. 2 ft. (length) × 1 ft. square feet.-How many, then, does it contain? (breadth)

=

= 2 sq. ft.

Q. If a figure 1 inch in breadth and 1 inch in length contains 1 square in h hoo many square inches will a figure 1 inch wide and 2 inches long contain? 3 inches long? 4 inches long? 8 inches long? 12 inches long? 20 inches

long?

Q. If a figure 1 foot wide and 1 foot long contains 1 square foot, how many square feet will a figure 1 foot wide and 2 feet long contain? 3 feet long 4 feet long? 8 feet long? 10 feet long?"

Q. How, then, do you proceed to find the square feet, inches, &c. of a square or parallelogram? A. Multiply the length by the breadth.

1. How many square feet in a room 10 feet long and 2 feet wide? (10 × 2=20 sq. ft., Ans.) In a room 8 feet wide and 12 feet long? 20 feet long?

2. How many square rods in a 8 rods long? 10 rods long? 10 rods long and 4 rods wide?

piece of land 4 rods wide and 11 rods long? 12 rods long?

Q. When a piece of land, in any shape, contams 40 square rods, what is it called? A. 1 rood.

3. How many square rods in a piece of land 40 rods long and 2 rods wid!?

4 rods wide?

Q. When a piec! of land, in any shape, contains 160 square rods, what is it called? A. 1 are.

4. How many square rods in a piece of land 20 rods long, and 2 rods wide? How many such pieces will make an acre or 160 square 1ods?

5. How wide must a piece of land be, which is 80 rods long to make an acre? 40 rods long? 20 rods long?

6. How many square feet of boards are contained in the floor of a room 10 feet square? 20 feet square? 10 feet wide and 20 feet long? 20 feet wide and 30 feet long

7. How many square yards in a figure 3 feet long and 3 feet wide? 6 feet square? 10 feet long and 9 feet wide? 6 fect long and 2 feet wide? (2 × 6 = 12÷9 = 14 yds., Ans) In a figure 10 feet long and 4 wide? A. 4 yds.

8. How many square yards in 9 square feet? In 108? In 72? In 99? In 27? In 80? In 37?

How, then, must square feet, square inches, &c. be divided? 4. Square inches by square inches, square feet by square feet,

&c.

Q. We are now prepared to answer that interesting question which occurs in geography, viz. the difference between miles square and square miles. The figures on the right are introduced for the purpose of its illustration Examine them attentively, then tell me, for instance, What is the difference between 5 square miles and 5 miles squarc? A. 5 square miles means 5 miles in length and only 1 in breadth; but 5 miles square means 5 miles in length and 5 miles in breadth, making 5 times as many miles as only 1 in Dreadth; that is, 25 square miles.

5 square miles

5 miles square

containing 25 square miles

From these illustrations we derive the following general

RULE.

I. How do you proceed to find the contents of a square or parallelogram? A. Multiply the lengtli by the breadth.

Exercises for the Slate.

1. In a room 16 feet long and 11 feet wide, how many square feet? A. 176.

2. How many acres in a piece of land 560 rods long and 32 rods wide? 560 × 32: 112 square acres, Ans.

The pupil must recollect that square inches must be divided by square inches, square yards by square yards, &c

3. How many acres in a piece of land 370 rods wide and 426 rous long? A. 985 acres, 20 rods.

4. How many rods long must a piece of land be, which is 80 rods wide, to make 1 acie? (2) How many rods wide to make 4 acres? (8) How many reds wide to make 200 acres? (400` 4 410 rods.

5. How many square feet of boards are contained in the floor of a room 40 ft. 6 in. lorg and 10 ft. 3 in. wide? (Reduce the inches to the decimal of a foot.) A. 415,125 tt.=415 feet.

4. How many acres are contained in the road from Boston to Providence, allowing the distance to be 40 miles, and the average width of the road 4 rods? A. 320 acres.

7. How many square feet are contained in a board 12 inelies long and 12 inches wide? () 12 inches wide and 24 inches long? (2) 3 fect long (3) 20 feet long? (20) A. 26 feet.

. How many square feet in a board 1 ft. 6 in. wide and 1> Ain. long? A. 28,125 ft.: 28 feet.

How many yards of carpeting, that is 14 yd. wide, will cover a floor 21 ft. 3 in. long and 13 ft. 6 in. wide?

A. 25 yards.

10. How many feet of boards will it take to cover the walls of a house 30 ft. 6 in. wide, 40 ft. 9 in. long, and 20 ft. high? and what will they come to at $10 per 1000 feet? A. 2850 feet; cost $284.

11. How many shingles will it take to cover the roof of a barn 40 feet long, allowing the length of the rafters to be 16 ft 6 in., and 6 shingles to cover 1 square foot? what will they cost, at $1,25 per 1000? A. 7920 shingles; cost $9,90.

12. What will a lot of land, 300 rods wide and 600 rods long come to, at $15 an acre? A. $16875.

13. What will a lot of land, 1 mile square, come to, at $20,75 per acre? A. $13280.

¶ LXXX. SOLID, OR CUBIC MEASURE.

QWhen a block is 1 inch long, 1 inch thick, and 1 inch wide, how many solid inches is it suud to contain? A. 1 solid or cubic inch.

Q. How many solid feet does a block, that is 1 foot long, 1 foot thick, and 1 foot wide, contain? A. 1 solid or cubic foot.

Q. If a block 1 foot thick, 1 foot wide, and 1 foot long, contains 1 solid foot, how many solid feet does such a block that is 2 feet long contain? 3 feet long? 5 feet long? 10 feet long? 20 feet long? 30 feet long?

Q. Hoo many solid feet does a block 2 feet long, 2 feet thick, and 1 foot cide, contain? 2 feet wide? 3 feet wide?

Q. How many solid inches does a block 3 inches long. 2 inches wide, and i tren thick, contain? 2 inches thick? 4 inches thick? 10 inches thick?

Q. How, then, would you proceed to find how many solid feet, inches, &c. are contained in a solid body? A. Multiply the length, breadth and depth together.

1. How many solid feet in a block 4 feet thick, 2 feet wide, and 5 feet long? Ans. 4 X 2 x 5= 40 solid feet.

2. How many solid or cubic feet in a block 12 inches long, 12 inches wide, and 12 inches thick .9. 1 solid foot.

Q. When a load of wood contains 128 solid feet, what is it called? A. 1 cord

3. How many solid feet in a pile of wood 8 feet long, 4 feet wide, and 4 feet high? A. 128=1 cord. How many cords of wood in a pile 8 feet long, 4 feet wide, and 8 feet high?

A. 256 solid feet= 2 cords.

Q. In common language, we say of load of wood brought to market, if it is 8 feet long, 4 feet high, and 4 feet wide, that it is a cord, or it contains 8 feet of wood. But this would make 128 solid fect; what, then, is to be understood by saying of such a load of wood, that it contains 8 feet of wood? or, in common language, there is 8 feet of it."

4. As 16 solid feet, in any form, are of 128 feet, that is, of a cord, it was found convenient, in reckoning, to call every 16 solid feet 1 cord foot; then, 8 such cord feet will make 128 solid feet, or 1 cord, for 8 times 16 are 128.

Q. How, then, would you bring solid feet into cord feet? Divide by 16.

4. How many cord feet in a pile of wood 8 feet long, 2 feet high, and 1 foot wide? How many in a load 8 feet long, 2 feet high, and 2 feet wide 8 feet long, 4 feet wide, and 2 feet high?

5. If, in purchasing a load of wood, the seller should say that t contains 3 cord feet, how many solid feet must there be in the load? How many solid feet to contain 4 cord feet? 5 ccrd feet? 6 cord feet? 7 cord feet? 8 cord feet? 9 cord feet?

6. How many cord feet in a pile of wood 8 feet long, 1 foot wide, and 4 feet high?

In performing this lust example, we multiply 4 feet (the height) by 1 foot the width) making 4; then, this 4 by 8 feet (the length), making 3216 (cord feet), cord feet, Ans. But, instead of multiplying the 4 by the 8 feet in length, and dividing by 16, we may simply divide by 2, without multiplying, for the divisor, 16, is 2 times as large as the multiplier, 8; consequently, it wil produce the same rosult as before, thus: 4X1422 cord feet, Aus us before.

Q. When, then, a loud of wood is 8 feet long, or contains troo lengths, each 4 feet (which is the usual length of wood prepared for market,) what easy method is there of finding how many cord feet such a load contains? A. Multiply the height and breadth together, and divide the product by 2.

7. How much wood in a load 8 feet long, 3 feet high, and 2 feet wide? 3× 2=6÷-2=3 cord feet, Ans.

8. How many cord feet in a load of wood 2 feet high, 2 feet wide, and of the usual 'ength? 3 feet high and 2 feet wide? 3 feet wide and 3 feet nigh? 4 feet wide and 4 feet high? 4 feet wide and 6 feet high? How many cords in a load 4 feet high, 4 feet wide?

9. How wide niust a load of wood be, which is 8 feet long and 1 foot high, to make 1 cord foot? How wide to make 2 co, d feet? eord feet? 6 cord feet? 10 cord feet?