Geometry. 262. THE AREA OF A RECTANGLE. 1. One side of every rectangle may be regarded as its base. The side perpendicular to its base is its altitude. 2. The number of square units in the row of square units next to the base of a rectangle, taken as many times as there are linear units in number of square units in its area. have 4 sq. units × 3 12 sq. units. = its altitude, equals the In the figure given, we NOTE 1.-In the above, it is assumed that the base and altitude are measured by the same linear unit, and that the sq. unit takes its name from the linear unit. NOTE 2. In the actual finding of the area of rectangles for practical purposes, the work is done mainly with abstract numbers and the proper interpretation is given to the result. There can be no serious objection to the rule for finding the area of rectangles, as given in the old books, provided the pupil is able to interpret it. RULE.-To find the area of a rectangle, “multiply its base by its altitude." PROBLEMS. 1. Find the area of the surface of a cubical block whose edge is 9 inches in length. 2. Find the area in square yards, of a rectangular piece of ground that is 36 feet by 45 feet. 3. Find the area in acres, of a rectangular piece of land that is 92 rods by 16 rods. 4. Find the area in square rods of a piece of ground that is 99 feet by 66 feet. 5. The area of a field 30 rods square is how many times as great as the area of a field 10 rods square? 263. MISCELLANEOUS REVIEW. 1. Clarence Marshall wished to borrow some money at a bank. He was told by the president of the bank that they (the bank officials) were discounting good 30-day paper at 7%. Mr. Marshall's name being regarded as "good," he drew his note upon one of the forms in use at the bank, for $1000 payable in thirty days without interest. On the presentation of this note to the cashier, how much money should he receive? 2. If Mr. Marshall's note described in problem 1 was dated April 10, 1898, (a) when must it be paid? (b) How much money will he pay when he "takes up" the note? (c) Does he pay for the use of the money borrowed, at the rate of exactly 7 % per annum ? 3. If a bank is discounting at 7 %, how much should be given for a note of $200 due in two months from the time it is discounted and bearing interest at the rate of 6% per annum from the date of discounting? 4. Find the value at the time of settlement of the following note: 5. What principal at 6 % will gain $6 in 1 year 4 months? 6. What principal at 6% will amount to $81 in 1 year 4 months? 7. Find the area in square feet, of a walk 4 feet wide around a rectangular flower bed that is 40 feet long and 12 feet wide. STOCKS AND BONDS. 264. Some kinds of business require so much capital that many persons combine to provide the necessary money. Such a combination of men organized under the laws of a State, the capital being divided into shares, is known as a corporation, or stock-company. Those who own the shares are called stock-holders. The stock-holders elect from their own number, certain men to manage the business. These managers are called directors. 265. The nominal value of a share is its face value; that is, the sum named on its face. Large corporations, usually, though not always, divide their capital into $100 shares. If the business is prosperous, shares may sell on the market for more than their nominal value. The stock is then said to be "above par," or "at a premium." If the business does not prosper, the shares may sell on the market for less than their nominal value. The stock is then said to be below par," or "at a discount." 266. If the business is profitable, a part of all of the earnings is periodically divided among the stock-holders. The sum divided is called a dividend. Dividends are always reckoned on the nominal or par value of the stock. If a corporation declares a 2 % dividend, it pays to each stockholder a sum equal to 2 % of the nominal value of the stock which he owns. 267. The kinds of business which are usually conducted by corporations, are: The mining of coal, silver, gold, etc.; the operation of gas works, railroads, large manufacturing establishments of all kinds, creameries, etc. 1. Examine the above certificate. What part of the entire stock of the Werner School Book Company would the owner of one hundred shares have? 2. A 3 % dividend would require how much money from the treasury of the Company? How much money should the owner of one hundred shares receive? 3. If the owner of five hundred shares sold his stock at a premium of 8% how much should he receive for it? 4. If a 4 % dividend is declared how much money should the owner of seven hundred and fifty shares of stock receive as his share of the dividend? Stocks. 268. HISTORY OF A STOCK COMPANY. The farmers of a certain community agreed to combine in the building and management of a creamery. It was determined that a capital of $5000 was necessary. This was divided into 50 shares of $100 each. Men then came forward and contributed as follows. A took 5 shares and paid in $500. G took 10 shares and paid in $1000. H, I, J, K, L, M, N, O, P, Q, R, S, & T, took 1 share each and paid in $100 each. (a) At the end of the first year the directors declared an 8 % dividend. How much did A receive? B? C? K? (b) What was the entire amount of the money divided among the stock-holders at the end of the first year? (c), Soon after this dividend was paid, A sold his stock to X at a premium of 10 %. How much did A receive for his stock? (d) At the end of the second year the profits were found to be comparatively small, and the directors could pay only a 3% dividend. How much did X receive? B? C? K? (e) What was the entire amount of the money divided among the stock-holders at the end of the second year? (f) Soon after this dividend was paid, B, C, D, E, and F, sold their stock to Y at a discount of 10 %. How much did this stock cost Y? (g) At the end of the third year, the profits were so small that no dividend was declared. The stock-holders became |