2. Multiply: 1. 5 bu. 2 pk. 6 qt. by 8. 2. 6 gal. 2 qt. 1 pt. 3 gi. by 7. 6. 3 T. 6 cwt. 59 lb. 14 oz. by 9. 8. 23 cu. yd. 16 cu. ft. 1226 cu. in. by 7. 14. 6 yr. 5 mo. 15 da. 18 hr. by 5. 15. 6 T. 12 cwt. 95 lb. 12 oz. 9 dr. by 8. 5. 53 lb. 9 oz. 16 pwt. by 10. 12. 42 gal. 1 qt. 1 pt. 1 gi. by 12. MEASUREMENT OF SURFACES. 1. A square has been defined. 2. Describe a square inch. Describe a square foot. 3. A figure 2 inches long and 1 inch wide, with all its angles equal, contains how many square inches? 2 3 Rectangle. 6. A figure 3 in. long and 2 in. wide contains how many square inches? 7. That is 3, the length, X 2, the width, = what? 8. The number of square units in a figure equals the product of what? 9. The number of square units in a figure is called its Area. 10. A figure with four sides and four right angles is called a Rectangle. PRINCIPLE. The area of a rectangular surface is the product of its length and width. FORMULA. Area of a Rectangle = Length x Width. PROBLEMS. 1. Find the area of a rectangular lot whose length is 33 ft. and width 6 ft. 6 in. The process requires that the length and width be expressed in the same denomination. 2. A room is 24 ft. long and 18 ft. wide. What is its area? 3. A floor is 10 ft. wide and 30 ft. long. Find its area. 4. The side wall of a room is 17 ft. long and 12 ft. high. How many square feet in the wall? How many square yards? How 5. An end wall of a room is 12 ft. by 12 ft. many square feet in the wall? How many square yards? 6. I have a rectangular room. Its length is 20 ft., its width, 18 ft.; its height, 12 ft. its height, 12 ft. Find the number of square feet and square yards in the four walls. Suggestion: The distance around the room × the height the area. 7. A rectangular field is, in length, 150 rods; in breadth, 130 rods. Find the number of square rods in the field and also the number of acres. 8. A room is 25 ft. long and 15 ft. wide. Find the area of both ceiling and floor; also the cost of plastering the ceiling, at 25 cents per square yard. 9. Find the cost of painting the walls and ceiling of a room 16 ft. 6 in. long, 15 ft. 9 in. wide, 14 ft. high, at 25 cents per square yard. 10. Find the area of a square field whose side is 76 rods. 11. Find the value of a field 180 rds. long and 90 rds. wide, at $20 an acre. 12. A room 18 ft. wide and 24 ft. long was covered with carpet, 1 yd. wide, at $1.00 per yard. How much did the carpeting cost? 13. I have a rectangular field 180.5 rds. long and 97.75 rds. wide. How many acres does it contain? 14. What will be the cost of cementing the floor of a cellar 56 ft. by 45 ft., at $.30 per square yard? 15. What will it cost to pave a street 3 mi. 115 rds. long and 2 rds. wide, at $46.50 per square rod? 16. How many square rods in a garden that is 7 rods square? 17. How many acres in a rectangular field 36 rds. 12 ft. wide, and 48 rds. 8 ft. long? 18. What is the cost of asphalting a walk 934 ft. by 61 ft., at $.75 per square yard? 19. A side of a public square is 660 ft. How many acres does it contain? 20. If a carpet is 36 in. wide, how many yards of it will be required to carpet a room 18 ft. by 16 ft? What will be the cost at $1.121 per yard? 21. Draw a figure to show the difference between 6 square feet and 6 feet square. We will call them square feet. If you place a cubic foot of wood or stone upon each square, how many cubic feet will you have? If upon those you place 12 more cubic feet, you will have how many cubic feet? If you add a third layer of 12 cubic feet, how many will you have? If you add a fourth layer, how many? add a fifth layer, how many? If you How many feet high is your structure now? The base layer has how many cubes? Therefore, the number 12, the base, X 5, the height, gives you what? A Rectangular Solid stands on a rectangular base and its angles are all right angles. The Volume of a solid is the number of cubic units it contains, i.e., of cubic inches, cubic feet, cubic yards. |