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LENGTHS AND SURFACES
Lines that meet, making a square corner, form a right angle.
A figure that has four straight sides and four right angles is called a rectangle.
A rectangle having its four sides equal is called a square. Rectangles that are not squares are sometimes called oblongs.
144 sq. in.=1 sq. ft.
9. sq. ft. =1 sq. yd.
1. What is the perimeter or the distance around a surface ?
2. What is meant by drawing a surface on a scale of 1 inch to 2 feet? On what scale is this surface drawn ? 4 in.
What is the unit of measure ?
units are there in the non
first row of squares ? in the second ? How many square inches are there in the rectangle, or what
is its area ? 2 x 4 x 1 sq. in. = 8 sq. in., area. The area of a rectangle is a number of square units equal to the product of its two dimensions when expressed in like units.
Thus, if the dimensions of a rectangle are 2 inches and 4 inches, the area is 8 square inches; if the dimensions are 2 feet and 4 feet, the area is 8 square feet.
1. If a pane of glass is 10 inches by 12 inches, how many square inches does it contain ?
2. How many square feet of glass equal 32 such panes ?
3. A garden is 73 feet by 50 feet. How many square feet does it contain ?
4. The page of a book is 77 inches by 5 inches. How many square inches are there in one side of such a page ?
5. How many square inches are there in a page of your book ?
6. Measure the blackboard in your schoolroom and find how many square feet it contains.
NOTE.— Reduce inches to the fraction of a foot; as, 8 ft. 6 in. = 84 ft.
7. How many square inches are there in the surface of your schoolroom door?
8. At $1} per square yard, how much will it cost to cover a floor 12 feet by 15 feet with linoleum ?
9. A plate glass window is 9 feet 8 inches wide and 12 feet 3 inches long. How much will such a window cost at $0.36 per square foot ?
10. Brussels carpet is 27 feet wide. How many square feet are there in a yard of it?
11. A room is 16 feet long and 14 feet wide. How much will it cost to paint the ceiling of this room at 12 & per square foot?
12. Which is the larger, a surface 26 in. long and 5 in. wide or a surface 11 in. long and 12 in. wide ?
13. At 15$ per square foot, how much does a sidewalk 50 feet long and 5 feet wide cost ?
14. At 12 & per square foot, how much will it cost to cement the floor of a cellar 28 ft. 4 in. by 22 ft. 6 in. ?
15. At $1.05 per square yard, how much will it cost to pave the street in front of a 50-foot lot, the street being 33 feet wide between the curbs ?
16. Compare a square 1 inch on a side with a square 2 inches on a side. Prove your work by drawing the required squares and dividing them into square inches.
17. Compare a rectangle 2 inches by 8 inches with a rectangle 4 inches by 16 inches.
18. Show that a square 4 inches on a side is 16 times as large as a square 1 inch on a side.
19. Name and draw the figures you have learned in which all the angles are right angles.
20. What other name is sometimes given to a rectangle ? Is a square a rectangle? When is a rectangle not a square ? Draw figure to illustrate.
21. Name the different measures of length.
22. Lines have what dimensions ? Surfaces have what dimensions ? Illustrate each.
5. How many square surfaces has it? A solid with six equal square surfaces is a cube.
6. Look at the figure and tell how many edges it has. What is the length of each edge ? A cube whose edge is 1 inch is called a cubic inch. 7. Draw on paper or on the blackboard a square foot.
8. Divide each side into 12 equal parts and connect them by straight lines.
9. How many square inches equal a square foot ? 10. The base of a 1-inch cube has how many square inches ?
11. 144 cubes 1 inch on an edge can be placed on a surface of 1 square foot thus :
12. What is the height of 12 such layers of cubes ? How many cubic inches are there in the first layer ? in 12 layers ?
13. How many cubic inches can be placed in the cube?
1728 cubic inches (cu. in.)=1 cubic foot (cu. ft.)
1. How many feet on an edge is the cube in the figure above ?
2. How many cubes 1 foot on an edge are there in the first layer ?
3. How many cubes 1 foot on an edge are there in the 3 layers ?
The contents of any body that has six rectangular surfaces is a number of cubical units equal to the product of its three dimensions when expressed in like units.
4. A schoolroom is 30 ft. wide, 40 ft. long, and 16 ft. high. Find the number of cubic feet of air in it.
5. Find the number of cubic yards of air in the room.
6. A piece of timber is 1 ft. square at one end and 12 ft. long. How many cubic feet are there in it?