2. Draw a diagram of a right-angled triangle whose base is 12 rd. and altitude 6 rd., drawing to a scale of 1⁄2 in. to a rod. Find its area.

3. Compare the area of the above triangle with the area of a rectangle 12 rd. long and 6 rd. wide.

4. The length of a rectangle is 80 rd. The length of its perimeter 220 rd. Find the width of the rectangle, and its area. Draw a diagram on a scale of 1 in. to 20 rd.

5. How many square yards of paper will be needed to cover the walls and ceiling of a room 18 ft. long, 15 ft. wide, and 12 ft. high?

6. At 3 a square foot, how much will it cost to sod a lawn 2 rods square?

7. Draw a diagram representing a triangle whose area is 24 sq. in.

8. Draw a diagram representing a triangle whose area is 1 acre.

9. Draw a rectangle representing an area of 2 acres. 10. How wide must a board 16 ft. long be to contain 12 sq. ft.?

11. How much will it cost, at 12 a square foot, to lay a sidewalk, 8 ft. wide, around a rectangular plot of ground 1000 ft. by 600 ft.?

12. Show by a diagram the difference between 3 inches square and 3 square inches.

13. How many square feet of land are there in a building lot 25 ft. wide at one end, 20 ft. at the other, and 200 ft. deep?

LESSON 116

A Circle is a plane figure bounded by a curved line, called its Circumference, every part of which is equally distant from a point within, called

the center.

The Diameter of a circle is a straight

line drawn from any point in the 4 circumference, through the center, and terminating in the circumference opposite, as AB.

The Radius of a circle is a straight

CIRCLE

D

line drawn from the center to the circumference, as CD.

B

1. Draw on the blackboard a circle having a diameter 7 in. long. With the aid of a string, or tape line, get the length of the circumference of your circle. Divide the circumference by the diameter. Do you find that the circumference is about 3 times the diameter?

2. Can you tell how to find the circumference when the diameter is given?

3. Find the circumference when the diameter is 8 inches; 12 inches; 24 feet; 20 yards; 12 rods.

4. Find the circumference when the radius is 3 inches; 5 inches; 2 yards; 1.75 rods.

5. If the circumference equals the diameter multiplied by 3, how would you find the diameter when the circumference is given?

6. Find the diameter when the circumference is 44 inches; 66 feet; 90.2 yards; 11,044 rods.

7. Find the circumference of a circle whose diam. is 1 rd.

8. What is the diameter of a circle whose circumference is 18 feet?

LESSON 117

Area of a Circle. The area of a circle can be found by multiplying the circumference by one half of the length of the radius.

According to this rule, we regard the area of the circle as equal to the sum of the areas of a number of equal triangles. If there were only eight of these triangles, as in Fig. 1, it is evident there would be considerable difference between the sum of the areas of the triangles and that of the circle. But if the number of triangles were increased to thirty-two, as in Fig. 2, the sum of the areas of the triangles would approach much nearer the area of the circle.

If the number of triangles were still further increased, they would form a plane figure that could hardly be distinguished from the circle. Now the sum of the areas of the triangles can be found by multiplying the sum of their bases by one half of their altitude. Therefore the area of a circle can be found by multiplying its circumference by one half of its radius.

Suppose the radius of a circle to be 3 inches.

Then the circumference = 3 × 2 × 3 =

189 in.

18 × = 28 sq. in.

following circles when the 5.5 feet; 6.25 rods.

2. Find the areas of the following circles when the diameter is 10 in.; 14 ft.; 28 yd.; 16.8 rd.

3. Find the circumference of a circle whose diameter is 42 feet.

Find the area.

4. A horse is tied to a tree by a rope 20 ft. long. Over what area can he pasture?

5. What is the area of a circle whose circumference is of a mile?

1. How many sides, or faces, has the cube? Of what shape are they? How do the six faces compare in size? 2. How many edges has the cube? How many corners?

3. How many edges bound each face? Does each edge form a part of the boundary of more than one face? If so, of how many faces?

4. How many corners has each face of the cube?

5. How many faces of a cube are parallel to any one face? How many edges are parallel to any one edge? The figure above represents a cubic inch.

A cubic inch is a cube each of whose edges is one inch long.

For definition of cube, see p. 108.

6. How high is a cubic foot? How wide? How long? 7. Define a cubic foot.

8. Define a cubic yard.

9. What is the area of a cubic inch?

10. What is the area of a cube each of whose edges is 2 in. long?

11. What is the area of a cube each of whose edges is 4 in. long?

A solid bounded by six rectangular faces is called a Rectangular Solid.

12. How many edges has this figure? corners?

How many

13. In what particular respect does the above figure resemble the cube? In what respect does it differ from the cube?

14. If the above figure is 4 in. long, 2 in. high, and 2 in. wide, what is the area of one end? Both ends? What is the area of one side? Of the four sides? What is the total area?