59. Cost of building a wall of stone 24 ft. long, 7 ft. high, 2 ft. thick, at $4.62 per perch?

60. How many bricks in a wall 24 ft. long, 8 ft. high, 3 ft. thick?

61. How many bricks in a pile 40 ft. by 20 ft. by 12 ft.? 62. Find the cost of brick necessary to build a wall 80 ft. long, 60 ft. high, 24 ft. thick, at $8 per M.?

63. Cost, at $9.50 per M., of the bricks necessary to build the walls of a house in the form of a rectangle, 40 ft. long, 32 ft. high, 24 ft. wide, the walls 2 ft. thick?

NOTE.-Take the outside measurement, which is given. Make no allowance for doors or windows. This will give the mason's measurement, which is rather greater than the actual measurement. There are 21 bricks in a cubic foot, allowing for mortar.

64. How many cu. in. in 40 gallons?
65. How many cu. in. in 5 bbl.?
66. How many cu. in. in 1 hhd.?
67. How many cu. in. in 5 bushels?
68. How many cu. ft. in 20 bushels?

69. How many gal. in a box 40 in. by 24 in. by 18 in.? 70. How many gal. in a box 3 ft. by 2 ft. by 14 ft.? 71. How many gal. in a tank 8 ft. by 6 ft. by 4 ft. 72. How many bushels may be contained in a bin 20 ft. by 8 ft. by 12 ft.?

MENSURATION OF PARALLELOGRAMS.

217. A Parallelogram is a plane four-sided figure, whose opposite sides are parallel and equal.

D

AE

F

A B C D is an oblique angled parallelogram.

Squares and rectangles are varieties of the parallelogram.

218. The Base of any plane figure is the side upon which it is supposed to rest. Parallelograms are

considered as having two bases, called upper and lower bases.

A B and C D are the bases of the parallelogram A B C D.

219. The Altitude of a parallelogram is the perpendicular distance between its bases.

EF is the altitude of the parallelogram A B C D.

In rectangles, either end or side is the altitude, because the end or side is perpendicular to the base.

220. The area of a parallelogram is equal to the product of its base and altitude.

1. Find the area of a parallelogram having a base of 12 ft., altitude of 8 ft.

2. Find area of parallelogram having base 50 ft., altitude 25 ft.

MENSURATION OF TRIANGLES.

221. A Triangle is a plane figure bounded by three straight lines.

A B C is a triangle. C B is its base; the angle A, opposite the base, is its vertex; A D, the perpendicular distance from the vertex to the base, is its altitude.

B

222. The Diagonal of a parallelogram is the straight line joining two opposite angles.

EG is the diagonal of the rectangle E F G H. K M is the diagonal of the parallelogram K L M N.

223. The diagonal of a parallelogram divides the parallelogram into two equal triangles.

The triangles E F G and E G H are equal. The triangles K L M and K M N are equal.

W

The pupil may draw any triangle, and by annexing to it, in the manner shown, an equal triangle, may form a parallelogram.

224. Since the area of a parallelogram is equal to the product of its base and altitude; and since every parallelogram may be divided into two equal triangles having the same base and altitude as the parallelogram, it follows that The area of a triangle is one half of the product of its base and altitude.

Find the area of the following triangles:

1. Base 6; altitude 4.

2. Base 12; altitude 8. 3. Base 40; altitude 15. 4. Base 60; altitude 30. 5. Base 85; altitude 20.

6. The base of a triangle is 12; its altitude is 25. What is its area?

7. The area of a triangle is 625; its altitude is 50. What is its base?

8. The area of a triangle is 360; its base is 60. What is its altitude?

9. The area of a parallelogram is 360; its base is 60. What is its altitude?

REVIEW QUESTIONS.

Define parallelogram; triangle. Define base of parallelogram ; base of triangle. Define altitude of parallelogram. Define diagonal. How may the area of a parallelogram be found? Of a triangle? If a parallelogram and a triangle have same base aud altitude, how do their areas compare?

SECTION XII.

Art. 225.

PERCENTAGE.

Per Cent means hundredths.

1 per cent is o; 6 per cent is 180, etc.

226.

hundredths.

Rate per Cent means a certain number of

In the expression 6 per cent, 6 is the rate. The rate is the numerator of a fraction of which the denominator is always 100. Instead of the words per cent the sign % is frequently used.

227. Rate per cent may be written as a common fraction, as a decimal fraction, or as per cent.

Thus:

T=.01=1%; the last, 1%, is read, one per cent. 180=.06=6%.

71

100=.071⁄2 or .075=74%; the last is read seven and one half per cent. 18.124 or .125=124%.

188-1.25-125%.

180.005=4%, the last is read one half of one per cent.

Observe that the decimal point is not used when the words per cent are used, or when the sign % is used, unless a fractional per cent is meant. Thus, 5% equals .05, not .5%. .5% means 5 tenths of one per cent, and is otherwise written 1%, or .001.

228. The Base is the number of which the per cent

is computed.

229. The Percentage is that per cent of the Base which is indicated by the Rate.

1. A man having 500 bushels of wheat, sold 8% of it. How many bushels did he sell?

PROCESS. 500X.08 40.

SOLUTION. He sold .08 of 500 bushels, which is 40 bushels.

In this example 500 bushels is the Base; 8%

is the Rate per cent; 40 bushels is the Percentage.

Observe that this is but a simple problem in multiplication of decimals.

230. The Base is the Multiplicand..

The Rate per cent is the Multiplier.

The Percentage is the Product.

231. As in simple multiplication, if any two of these terms are given, the other may be found, since the Base and Rate are factors of the Percentage.

2. A man having 500 bushels wheat sold 40 bushels. What per cent. of his wheat did he sell?

PROCESS.

40 500.08.

SOLUTION.-An inspection of example 1 will show that 40 bushels is the product of two factors, the Base and the Rate. Dividing the product, 40, by the given factor, 500, the quotient is the Rate, 8%. 3. A man sold 40 bushels of wheat, which was 8% of what wheat he had. How many bushels had he?

PROCESS.

40.08 500.

SOLUTION.-Comparing this example with example 1 and 2, it will be seen that the factor required here is the Base. Dividing the product, 40, by the given factor, .08, the quotient is the Base, 500.