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3. What is the content of a board 14 feet by 15 inches?

Ans. 171 ft. 4. What is the content of a board 18 feet by 15 inches?

Ans. 221 ft.

TO MEASURE SCANTLING OR JOIST.

Rule.-Multiply the depth and width taken in inches by the length in feet, divide the product by 12, and the quotient is the content in feet.

1. How many feet are there in 3 joist, each of which are 15 feet long, 5 inches wide and 3 inches thick?

Ans. 564 feet. 2. How many feet in 20 joist 10 feet long 6 inches wide, and 2 inches thick?

Ans. 200 feet.

CASE II.

When a Board is wider at one end than the other. GENERAL Rule.—Take the breadth in the middle, or add the measure of both ends together, and take the sum for a mean breadth which multiply by the length for the content.

1. Suppose a board be 10 feet long and 10 inches wide at one end, and 34 inches wide at the other end, what is its superficial content?

Ans. 18 feet. Illustration, 34

10

1 sum, 44

22 medium or mean breadth.
10 feet long

12)220

18} feet answer; or, if the length be in feet and inches, reduce the length to inches, which being multiplied by the mean breadth in inches and divided by 144, we get the content in feet.

Q. Why do we divide by 144?

A. Because, when we multiply inches by inches, the product is square inches; therefore, we divide by 144, 144 square inches being to 1

square

foot. PAPERING ROOMS. There is a room papered, the compass of which is 47 feet 3 inches, and the height 7 feet 6 inches, what is the content in square yards?

Ans. 39f yds. CARPENTER’S WORK. Roofing, flooring, partitioning, and the principal carpentry in modern buildings, are measured by the

square

of 10 feet, that is 100 feet.

RULE FOR ROOFING.-Multiply the depth and half depth by the front, or, the front and half front by the depth, and you get the content. The dimensions are taken in feet and inches.

1. If a floor be 49 feet 6 inches long, and 26 feet 6 inches broad, how many square feet? ? Operation. 49.5

26.5

2475 2970 990

1311(75 Ans. 13,11 ft. 9 in. or 13s. 11f. 9i.

12

9900

BRICKLAYER'S WORK.
Bricklayers are generally paid by the day or perch.

1. Suppose a garden wall to be 254 feet round and 12 feet 7 inches high and 3 bricks thick, how many square rods does it contain?

Ans. 231 sq. rods. F. F. I. 254 +12.7 3196.2 X2 = 6392.4

234 sq. rods,

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Note.- As the standard thickness is 11 brick thick, then 161 feet long, 1 foot thick and 14 feet high = 24.75 feet, or 1 perch, hence we multiply the length, breadth and thickness of the wall together, and divide by 24.75 for the number of perches required.

DIGGING.
Cellars, vaults, clay for brick, canals, 8c., are measured

by the solid yard of 27 feet.
Rule.-Multiply the length, width and depth, together
and divide the product by 27, for the number of cubic
yards.

How many yards of digging in a cellar 25 feet long, 20 feet wide and 10 feet 6 inches deep? Ans. 1944 cub. yds.

Note.-A solid yard of clay will make 7 or 800 brick, and 31 bushels of lime and half a load of sand will be sufficient to lay 1000 brick. To find how many thousand brick will be required for

building a house of any given dimensions. Suppose a house of the following dimensions, viz: 84 feet long, 40 feet wide, 20 feet high and the walls to be 1 foot thick?

Ans. 105,408 bricks. Rule.-Deduct the thickness of the wall, from the length of each side, because the inner sides are 1 foot less in height than the outer sides. This rule is unquestionably correct.

OPERATION.

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84-1 = 83 feet and 40—1 = 39
Now 83 x 2 = 166 sum of 2 sides in length,
.and 39 X 2 78 sum of 2 do. in breadth,

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244
compass 20 feet in height.

4880 x 1728 = 8432640 cub. in. Now allowing a brick to be 8 inches long, 4 inches

wide, and 24 inches thick, there would be 80 cubic inches in a brick, hence 843264(0 105,408 brick, Ans.

8(0 2. How many thousand brick 8 inches long, 4 inches wide, and 21 inches thick, will build a wall in front of a church which is to be in compass 240 feet long, 6 feet high and 1 foot 6 inches wide? Ans. 51.840 bricks.

3. 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 feet 6 inches, and 6 shingles to cover 1 square foot; what will they cost at $1.25 per 1000?

Ans. 7,920 shingles; cost $9.90.

MENSURATION OF SUPERFICES AND SOLIDS.
PROBLEM 1.

ΑΙ

B В

To find the area of a square. Rule.-Square the side: and the product or rectangle will be the superficial C

D content. 1. A lot of ground is 10 perches square, what is the area? PROBLEM 2.

Ans. 100 ps. = 2 r. 20 p.

A 18 ft. Note.-A square is a parallelo

B gram, but a parallelogram is not a square, because it is an oblong whose length and breadth are unequal.

С 2. What is the content of a board 15 feet long and 2 feet wide?

Ans. 30 feet. 3. What is the difference between a floor 40 feet square and 2 others, each 20 feet square?

Àns. 800 feet. 4. There is a square of 3600 yards area; what is the side of a square, and the breadth of a walk along each side of the square at each end, which may take up just one half the square?

Ans. 42.42 + yds. side of the sq. 8.78 + yds, breadth of walk.

A

PROBLEM 3.

B To find the area of a rhombus. Rule.--Multiply the length of the base by the perpendicular height.

5. The base of a rhombus is 14 C feet C and its height 6 feet, required the area?

Ans. 84 feet.
PROBLEM 4.
To find the area of a triangle.

C
Rule.—Multiply half the base
by the perpendicular height, or if
the perpendicular is not given, A

B add the three sides together, take

D half that sum, subtract each side severally; from the hali sum multiply the half sum and the three differences together, and the square root of the product will be the area.

1. Required the area of a right angled triangle whose base is 40 and perpendicular 30 perches? Ans. 600.

2. Required the area of a triangle whose sides are 10, 12 and 18 perches respectively? Ans. 56.57 perches.

PROBLEM 5.

CASE I.

Diameter

By having the diameter of a circle to

find the area. Rule.-Square the diameter, and multiply the product by .7854 for the

area.

CASE II.

By having the circumference of a circle to find the area.

RULE.-Square the circumference and multiply that square by .07958. 1. The diameter of a circle is 24, required the area?

Ans. 452.4904. 2. The circumference of a circle is 80, required the area?

Ans. 509.312.

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