If through the vertices B and C lines are drawn parallel respectively to AC and AB, the parallelogram ABEC is formed.

8. How does the triangle ABC compare with BEC? What part of the parallelogram ABEC is the triangle ABC? How then can the area of a triangle be found?

9. What is the area of a triangle whose base is 24 feet and the altitude 20 feet?

10. What is the area of a triangle whose base is 15 feet and altitude 12 feet?

11. The area of a triangle is 130 square feet and the base is 13 feet. What is the altitude?

12. If the area of a triangle is 48 square feet, and the altitude is 8 feet, what is the base?

The line BC in the last figure is called the diagonal of the parallelogram ABEC. In a rectangle the diagonal is equal to the square root of the sum of the squares of the base and the altitude.

13. What is the diagonal of a rectangle 3 by 4 feet? 6 by 8? 9 by 12? 5 by 12?

14. If the diagonal of a rectangle is 10 feet and the base 8 feet, what is the altitude?

A board foot is a square foot one inch in thick

ness.

Boards less than an inch in thickness are reckoned the same as though they were an inch in thickness.

15. How many feet, board measure, in a plank 20 feet long, 15 inches wide, and 2 inches thick? 16. How many feet, board measure, in a board 12 feet long, 2 feet wide, and inch thick? 17. How many feet, board

measure, in a board 18 feet long, 4 inches wide, and inch thick? 18. Find the number of feet, board measure, in 5 joists 3 by 4 (that is, the two smaller dimensions of the joists are 3 inches and 4 inches), each 16 feet long.

19. What is the price of 50 boards, 20 feet long, 6 inches wide, and inch thick, at $22 a thousand (board) feet? What would be the price if the boards were twice as thick? If they were half as thick?

20. What is the price of 10 planks, each 16 feet. long, 15 inches wide, and 2 inches thick, at the rate of $25 a thousand (board) feet?

21. Find the number of feet, board measure, in a stick of timber 50 feet long, 12 by 14 inches square. What is it worth at the rate of $20 a thousand (board) feet?

A circle is a plane figure bounded by a curved line

is the centre CD is the radius and AD the diameter. The circumference of a circle is about 22 or 3 of the diameter.

E

22. What is the diameter of a circle 44 inches in circumference?

23. What is the circumference of a circle whose diameter is 35 feet? Whose radius is 3 feet 6 inches ?

24. What is the radius of a circle whose circumference is 66 feet?

25. The circumference of a circle is 22 inches. What is the radius? What is the area?

The area of a circle is equal to half the product of its circumference by its radius.

26. What is the area of a circle having a radius of 14 inches?

27. The circumference of a circle is 66 feet. What is its area?

28. The diameter of a circle is 14 inches. What is its area?

CHAPTER LXIV.

A rectangular prism is a solid bounded

by six rectangles.

A cube is a rectangular prism bounded by squares.

The volume, or cubic contents, of a rectangular prism

Cube.

is equal to the product of its three dimensions.

1. What is the volume of a cube 5

inches in height?

2. What are the contents of the

rectangular prism (see Fig.) whose

Prism.

three dimensions are 2 feet, 3 feet, and 4 feet?

3. What is the length of a cubical block that contains 64 cubic inches? What is the area of one of its sides? How many square inches in the entire surface of the cube?

4. The contents of a cube are 27 cubic inches. What is the length of one side? How many square inches in its entire surface?

5. How many cubic feet of air are there in a room 15 feet long, 12 feet wide, and 10 feet high? 6. How many cords of wood are there in a pile 24 feet long, 4 feet wide, and 8 feet high?

7. A cord of wood is 8 feet long, 4 feet wide, and 4 feet high. How many cubic feet are there in a cord? How many square feet in the surface of a pile of wood 8 by 4 by 4 feet?

8. How deep is the excavation vat to contain 64 cubic yards? area of the top of the vat?

for a cubical

What is the

9. A farmer sells a load of wood, 8 feet long, 4 feet wide, and 6 feet high, at the rate of $6 a cord. How much does he receive for the wood? If he received $6 for the wood, what would be the price of a cord?

10. What is the volume of a cubical dish 10 by 10 by 10 inches? How many gallons, of 231 cubic inches each, will it hold?

11. A tin dish, without a cover, in the form of a rectangular prism, is 8 inches high and has a base 4 by 5 inches. How many gallons, of 231 cubic inches each, will it hold? How many square inches of tin are there in its surface.

12. Bricks are usually 8 inches long, 4 inches wide, and 2 inches thick. How many square

inches are there in the entire surface of a brick ? What is the least number of bricks that can be used to cover a square foot, or 144 square inches of surface? What is the greatest number? What other number may be used?