A 5. The Area of a surface is the number of square units it contains. 1 2 3 The area of the rectangle A. B. is 12 4 5 6 squares; they may be square inches, square feet, or square rods, etc. 9 Since there are 4 rows of 3 squares each, 12 squares, is denoted by the product 10 11 12 of 4 by 3; i.e., by the product of the length by the breadth. B If by 4, four squares are meant, is 3 to be considered an abstract or a denominate number? the area, FORMULA (Indicated Process). Area of rectangle Length x Breadth. NOTE. —The rule implies that the length and breadth are expressed in the same denomination. Common Square Measure. Table. 1 Square Yard (sq. yd.). 1 304 Square Yards 1 Perch. 160 Square Rods 1 Acre (A.). 1 Square Mile (sq. mi.). { ={ sq. mi. A sq. rd. sq. in. = 8q. ft. Scale : 144, 9, 30ḥ, 160, 640. Units. The unit for land is the acre ; for plastering, ceiling, etc., it is the sq. yd. ; for paving, glazing, and stone-cutting, it is the sq. ft.; for roofing, flooring, and slating, it is a square 10 ft. by 10 ft., or 100 sq. ft. Surveyors' Square Measure. Table. 625 Square Links (sq. 1.) : 1 Sq. Rd., or Percb (P.). 1 Sq. Chain. 1 Acre. 640 Acres 1 Sq. Mile. 36 Sq. Miles = 1 Township (Tp.). EXERCISES. 1. 54 A. 10 P. to perches (sq. rd.). . . Process. 7 160 Х 1 121 4 30 = 141 Х x x 144 = 4,878,720 sq. 9 . in. 14. [ of A. to units of lower denominations. g 1 Process. f A.=] of 160 sq. rd. 1244 sq. rd. sq. rd. = of 141 sq. yd. 134 sq. yd. . yd. 4 sq. sq. ft. sq. 15. A. to units of lower denominations. PROBLEMS. Indicate the process first, and abridge the work by cancellation. 1. A rectangular piece of land is 40 rd. long and 12 rd. wide. Find the acres in it. 2. A floor is 8 ft. by 16 ft. How many sq. ft. in it? 7. A fence surrounding a mile race-course is 6 ft. high. How many sq. yd. in it? Find the cost at 10 cents a sq. yd. 8. A room is 20 by 30 feet. How much will it cost to carpet the room with carpet 1 yd. wide at $1.00 per yd.? 9. A field contains 12 acres and is 24 rds. wide. Find its length. 10. I bought 10 acres of land at $200 an acre and sold it at 8 cts. a sq. ft. Find the gain. 11. Find the cost of a piece of oil-cloth 25 feet long and 16 feet 9 inches wide, at 95 cents a square yard. 12. What will it cost to carpet a room 18 feet long and 25% feet wide at $1.25 a yard, the carpet being å yd. wide ? 13. A school-room measures as follows: Length, 72 ft.; width, 22; ft.; height, 16 ft. Deduct 245 sq. ft. for doors and windows, and find the cost of plastering at 16) cts. per sq. yd. 14. Show the difference between 6 sq. ft. and 6 feet square. 15. A room is to be plastered and painted; its length is 20 ft., its width 18 ft., its height 12 feet; the rate will be 33} cts. per sq. yd. Find the cost of the work. 16. Find the value of a field 180 rd. long and 943 rd. wide at $18 an acre. 17. How many yds. of carpeting, 3 ft. 6 in. wide, will it take to cover a floor 21 ft. wide and 36 ft. long, the carpet running lengthwise ? 18. A room measures 18 ft. X 15 ft. X 10 ft. Find the cost of papering it with paper 24 in. wide at $.85 a roll, 8 yd. in a roll, making a deduction of 20 sq. yd. for openings. 19. A sidewalk is 10 ft. wide, exclusive of the curb, and is 100 ft. long. How many 4 X 8 bricks in it? 20. A 15 by 18 ft. room is to be carpeted. Which will be the cheaper way to run yard-wide strips, lengthwise or breadth wise? 21. A room is 18 ft. wide and 9 ft. high. After deducting from the area of one end two windows 6 ft. X 41 ft., find the number of sq. yd. remaining to be plastered. 22. A rectangular piece of land 1320 yds. long and 2 rods wide was taken for public use. How much was due the owner at $160 an acre ? 23. A barn is roofed with shingles put 6 in. to the weather. Find the cost at $12 per M. if the roof is 60 feet long, each side being 32 feet, the first course along the eaves being doubled. [1000 shingles to 110 sq. feet.] 24. Find the cost of slating a roof 64 ft. 9 in. long and 45 ft. wide at $15.371 per square. 25. How many bricks will pave a sidewalk 25 ft. by 10 ft., a brick measuring 8 in. X 4 in. X 2 in.? 26. How many bricks, set on end, will pave a sidewalk containing one-half the last area ? MEASURES OF VOLUME. 1. A Solid has length, breadth, and thickness. 2. A Rectangular Solid is bounded by six rectangular faces. a 3. A Cube has six equal faces and twelve equal edges. 4. Volume, or Solid Contents, of a body is the number of cubic units it contains. 5. If on a rectangle of 12 sq. ft., as a base, we erect a rectangular solid 5 feet high, the structure will contain 3 times 4, or 12, cubic feet for each of the 5 feet of height. Hence, the volume of the solid will be 5 times 12, or 60, cubic feet. RULE. The volume of a rectangular solid is the number of cubic units denoted by the product of its length, breadth, and thickness. NOTE.-The rule implies that the three dimensions are all of the same denomination. |