SQUARE OR SURFACE MEASURE Write the table of square measure. The area of a figure is the number of square units it contains. The figure represents a surface 4 feet long and 1 yard wide. What is its area? A surface 4 feet by 1 yard is a surface 4 feet by 3 feet. The shaded part represents the unit of measurement, 1 square foot. Second. Find the number of these units in one row. Third. Multiply the number of units in one row by the number of rows. Short method: 3 x 4 = 12. In finding areas the dimensions must be expressed in the same unit of measurement (inches, feet, yards, etc.). 1. What measurements must be made to find the area of one side of a sheet of examination paper? How is the area found? 2. Remembering that the multiplier is an abstract number simply showing how many times, explain just how to find the area of a piece of paper 8 in. long and 6 in. wide. 3. A geography covers 96 square inches on the table. It is 8 inches wide. How long is it? 4. A field is 9 rods long and as wide. What is its area? What is its perimeter? 5. One board is 16 in. by 4 in. Another is 8 in. square. Compare their areas. Compare their perimeters. 6. The area of a square lot is 49 square rods. What is its perimeter? 7. The perimeter of a square lot is 48 rods. What is its area? 8. A field is 8 rods long. It contains 32 square rods. How many rods of fence will inclose it? 9. What is meant by 2 square inches? 10. What is meant by a 2-inch square? 11. Mr. Chase has two square fields. One contains 64 square rods. The distance around the other is 64 rods. Compare their areas. Compare their perimeters. 1. What are the dimensions in feet of a 12-inch square? What is its perimeter in feet? Its area in square feet? 2. Make and fill out a table like the following: DIMENSIONS IN FEET PERIMETER IN FEET AREA IN SQUARE FEET SQUARES 12-inch 1 foot 24-inch 36-inch Continue with 48-inch, 60-inch, 72-inch, 84-inch, 96inch, 108-inch, 120-inch, 132-inch, 144-inch squares. 3. Mr. James has a lot of land containing 16 square rods. Express its area in acres. 4. Mr. Brown has a lot that is 16 rods square. Express its area in acres. 5. A lot 108 ft. by 75 ft. is sold at 12 cents a square foot. How much is received for it? 6. A lot of land is 66 feet wide and 11 times as long. (1) How many rods of fence will be required to inclose it? (2) What is the value of the lot at 18 cents a square foot? 7. How many feet of weather molding are necessary for a door 6' 10" by 3' 4"? What is the area of the opening when the door is wide open? Find the number of acres in lots of these dimensions: 20. Find the perimeters of the lots in examples 8 to 19. 21. A lot containing 2 A. 112 sq. rd. was cut up into 18 equal house lots. How many square rods in each lot? 22. Mr. Jackson paid $8000 for a lot 40 rd. by 30 rd. At the same rate what ought he to pay for another lot one half as long and one half as wide? 23. The garden of the Harvard school is 80 ft. by 60 ft. Each pupil has a plot 10 ft. by 5 ft. Allowing one sixth of the whole area for paths, how many individual gardens are there? Find the areas of the following rectangles : 44. Express the perimeters of the above rectangles in inches, feet, or yards, as directed. 45. If you were given your choice of three lots — 36 rd. by 9 rd., 27 rd. by 12 rd., and 18 rd. by 18 rd. — on condition that you pay for fencing, which would you choose? 46. The cost of fencing a lot at 22 cents per foot was $73.92. What was the perimeter of the lot? 47. A chess board is 8 squares long and 8 squares wide. Each square is 11 inches long. What is the area of the board? The distance around its edge? 48. What is the area of a table 2 ft. 8 in. by 2 ft. 8 in.? West A POULTRY HOUSE AND YARDS The diagram represents the ground plan of a poultry house and yards. North Find: South 1. The area covered by the house; by each compartment; the number of square feet of floor space to a fowl if there are 50 in a compartment. 2. The area of all the yards; of each yard; the yard space allowed to each fowl. 3. The total area covered by house and yards; the part of the total area covered by the house; by the yards. East |