CHAPTER XIV. MENSURATION. (PRACTICAL RULES.) 284. A surface has two dimensions: length and breadth, 285. A solid has three dimensions: length, breadth, and thickness. 286. The area of a surface is the number of units of surface which it contains, the unit of surface being a square which has a linear unit for each of its dimensions. 287. The volume of a solid is the number of units of volume which it contains, the unit of volume being a cube which has a linear unit for each of its three dimensions. 288. In writing the dimensions of surfaces and solids, the sign is used for the word by, an accent (') for the word feet, and two accents (") for the word inches. Thus, the dimensions of the floor of a room, 15 feet 6 inches long, 13 feet 8 inches wide, are denoted by 15' 6" x 13'8". The dimensions of a brick, 8 inches long, 4 inches wide, 2 inches thick, are denoted by 8" x 4" x 21". 289. Rectangle. The area of a rectangle equals the product of its length and breadth. (See page 165.) 290. The perimeter of a rectangle or of any other surface figure is the sum of the lengths of the lines which bound it. Ex. 163. 1. The floor of a room is a rectangle 15′ 6′′ × 18'. Find its perimeter and its area. 2. The ceiling of a room is a rectangle 16' x 20'. Find its perimeter and its area. 3. A rectangular field is 60 rods × 80 rods. Find its area in acres, and the cost of fencing it at $1.50 a rod. 4. How many boards 12 ft. long will be required to inclose a square field 48 rds. on a side with a fence 4 boards high? How many acres are there in the field? 291. Carpeting. Carpeting is sold by the yard in length. The common widths are a yard, and three-quarters of a yard. It will be remembered that in determining the number of yards of carpet for a room, we first decide whether the strips shall run lengthwise or across the room, and then find the number of strips needed. The number of yards in a strip, including the allowance for waste in matching the pattern, multiplied by the number of strips will give the required number of yards. (See page 169.) 5. How many yards of carpeting of a yard wide will be required for a floor 20′ × 17′ 6′′, if the strips run lengthwise, and if there is a waste of 9 in. a strip in matching the pattern? 6. How many yards of carpeting 1 yd. wide will be required for a room 18' 4" x 17' 8", if the strips run lengthwise of the room, and if there is a waste of 8 in. a strip in matching the pattern? Find the cost of carpeting the room if the carpet is worth 85 cents a yard, and 10 cents a yard is paid for making and laying. 7. Find the cost of the carpet for a room 19′ 8′′ × 17′ 10′′, if the carpet is of a yard wide and costs $1.75 a yard, the strips running across the room, and 9 in. a strip being wasted in matching the pattern. 292. Plastering. The unit for measuring painting, plastering, and paving is the square yard. The practice in painting and plastering is to find the total area within the bounding lines of the work, to deduct from this amount half the area of all doors, windows, and other openings, and to take as the net area the nearest whole number of square yards in the remainder. Ex. A rectangular room is 15' x 13'4" x 9'. The baseboard is 1 foot high; there is a door 7′ 4′′ × 4′, and two windows 6' x 4' each. Find the cost of plastering the walls and ceiling at 18 cents a square yard. 8. Find the cost of plastering the walls and ceiling of a room 17'4" x 15′ 8′′ × 10′ 4′′, at 20 cents per square yard, if 10 sq. yds. are deducted for doors, windows, and baseboard. 9. Find the cost of whitening the walls and ceiling of a room 16' 6" x 15' 6" x 9' 6", at five cents per square yard, deducting 12 sq. yds. for doors, windows, and baseboard. 10. Find the cost of plastering a room 18' x 15' x 10', at 30 cents per square yard, if the room contains one door 7'6" x 4', three windows each 6' x 4', and a baseboard one foot high around the room. 293. Wall Paper. Wall paper is 18 in. wide and is sold in single rolls 8 yds. long, or in double rolls 16 yds. long. In estimating the number of rolls of paper required for a room of ordinary height, find the number of feet in the perimeter of the room, leaving out the widths of the doors. and windows, and allow a double roll or two single rolls. for every 7 ft. Ex. How many double rolls of paper will be required for a room of ordinary height, 18′ × 16', with one door, and four windows, each 4 ft. wide? Perimeter of room = 2 x 18' + 2 × 16′ = 68' Deducting door and windows 48 = 7. = = 48/ 7 double rolls. Ans. 11. How many double rolls of paper will be required for a room of ordinary height, 18'4" x 16' 6", with two doors and three windows, each 4 ft. wide? 12. Find the cost of paper at 25 cents a single roll, and bordering at 8 cents a yard, for a room of ordinary height, 17'9" x 17'3", allowing for one door and four windows, each 4' 2". (No allowance for doors. and windows is made for the bordering.) 13. Find the cost of paper at 50 cents a single roll for a room of ordinary height, 20' 8" x 17'6", with two doors and three windows, each 4'2" wide. 294. Laths. Laths are put up in bundles, 100 pieces, each 4 ft. long, and a bundle is estimated to cover 5 sq. yds. In estimating the number of bundles of laths, deduct the whole area of all openings. Ex. How many bundles of laths will be required for the ceiling of a room 36 ft. square? 36 ft. 12 yds. = Hence ceiling contains 12 x 12 = 144 sq. yds. 144 = 29. 29 bundles. Ans. 14. How many bundles of laths will be required for the ceiling and walls of a room 26 ft. square, 14 ft. high, allowing 20 sq. yds for doors, windows, and baseboard? 15. How many bundles of laths are required for the ceiling and walls of a room 28′ × 32′ and 16′ high, allowing for three windows 8' x 3'6" each, and two doors 8' x 4'2" each, and a baseboard 1 ft. high? 295. Clapboards. Clapboards are 4 ft. long and are laid 3 or 4 in. to the weather. Ex. Find the number of clapboards required for the front of a house 42 ft. long and 22 ft. high, allowing 100 sq. ft. for doors and windows, and adding 10% |