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5. Cut from paper triangles like figure 2 and figure 3. Cut on dotted lines; arrange parts to form rectangles. Show that each triangle is equal to a rectangle whose base is equal to the base of the triangle and whose altitude is one half of the altitude of the triangle.

3

4" FIGURE 2

6"

FIGURE 3

The area of a triangle is equal to one half the product of its base and its altitude.

Find areas of these triangles:

[blocks in formation]

16. The base of a right-angled triangle is 8 feet and the

altitude is 5 feet.

What is the area?

17. The base and altitude of a triangle are each 16 inches. What is the area?

18. What is the area of a triangular lot of land whose base is 20 yards and whose altitude is 25 feet?

19. How many acres in a triangular lot of land whose base and altitude are, respectively, 40 rods and 24 rods?

20. Make up problems in finding areas and perimeters of triangles.

DRAWING TO SCALE

Written

1. Make a diagram of the top surface of the teacher's desk. Scale"=1'.

2. Make a diagram of the side of the teacher's desk facing the school, on a scale of 1" 1'.

=

3. Represent on paper the area of the schoolroom floor. Scale 1" 8'.

=

Compute the number of square feet in the floor.

Compute the cost of the floor boards at 6 cents per square foot.

4. Make a diagram of a picture 24" by 20" surrounded by a 2" frame. Scale"=2".

5. Make a diagram of the door leading from the schoolroom into the hall, on a scale of 1 inch = 1 foot.

6. Make a diagram of the lower sash of one of the schoolroom windows, letting 1 inch represent 6 inches. Compute the area of the lighting surface.

7. Draw a rectangle 2 inches by 1 inches. This figure represents the ground plan of a house drawn on a scale of inch to 4 feet. Find the dimensions of the house and the area covered by the house.

8. Four adjoining house lots are, respectively, 45 ft., 60 ft., 90 ft., and 75 ft. on the street side. Each lot is 120 ft. deep.

(a) Draw a diagram of the lots on a scale of 1 inch to 60 feet.

(b) Compute the values of the lots at 182 cents per square foot.

(c) What is the area of all the lots?

(d) What is the perimeter of each lot?

9. In many places building lots are sold by the street frontage. At $22.75 per front foot, what is the value of each lot in problem 8?

10. The diagram of a park covers a space 31" by 5". 1" represents 24 rods. What are the dimensions of the

park? Its area in acres?

11. On a scale of 1" to 1' make a diagram of a floor 16' by 12', and on it a rug 3 yd. by 2 yd. Compute the areas of the floor and of the rug in square feet.

12. Make a diagram of a mirror whose outside dimensions are 32 inches by 20 inches. Scale"= 1 foot.

13. Make a drawing of a 2-inch picture frame whose outside dimensions are 32 inches by 24 inches. Scale 1 inch to 8 inches.

14. Find from a geography map the distance from New York to Chicago. From Chicago to St. Louis. From St. Louis to Denver. From Denver to San Francisco.

15. Using some map in your geography, find the dimensions of the state of Colorado. Compute its area in square miles.

16. Find the dimensions and area of Wyoming. Of Kansas.

Of Utah. Of Nevada. Of other states.

Of Utah.

CUBIC OR VOLUME MEASURE

Oral

A volume or solid has three dimensions-length, width, and thickness.

A solid bounded by six rectangles is a rectangular prism. (Fig. 1.)

If the six rectangles are squares, the solid is a cube. (Fig. 2.)

[blocks in formation]

1728 cubic inches (cu. in.)= 1 cubic foot (cu. ft.)

27 cubic feet

=

1 cubic yard (cu. yd.)

A load of earth, sand, etc., is a cubic yard.

4. How many inch cubes can be cut from a cubic foot of wood?

5. What is the volume of a 2-inch cube?

6. A 2-inch cube is how many times as large as 2

cubic inches?

7. How many 1-inch cubes are required to build a 4-inch cube?

8. How many 2-inch cubes are equal in volume to a 4-inch cube?

9. How many blocks 1 inch × 1 inch × 1 inch can be packed in a box 4 inches x 2 inches x 3 inches?

10. A cubic foot is equal to how many 6-inch cubes? 11. A block of wood 8 inches long, 4 inches wide, and 2 inches thick will make how many 1-inch cubes?

12. A cake of ice 1 yard long, 1 yard wide, and 1 yard thick is cut into cakes 1 foot long, 1 foot wide, and 1 foot thick. How many?

13. A cubic foot is what part of a cubic yard?

14. Nine cubic feet are what part of a load of sand? 15. Thirty-six cubic yards are how many cubic feet? 16. Twenty-seven hundred cubic feet of earth are carted for filling. How many loads?

FINDING VOLUMES

Oral and Written

The volume of a solid is the number of cubic units it contains.

1. What is the volume of a rectangular prism 4 inches long, 2 inches wide, and 6

inches high?

Figure 3 represents the prism. Figure 4 represents 1 cubic inch. The problem is to find how many cubic units like figure 4 there are in figure 3.

The unit of measurement is 1 cubic inch.

FIGURE 3

FIGURE 4

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