11. What part of a ton is 480 lb.? 8.5 cwt.? 12 cwt. 50 lb.?

12. Find the cost of 15 yd. of cloth if 5ğ yd. cost $20ğ. 13. How far will a man walk in 4 hr. at the rate of 14 mi. in 31 hr.?

14. Mary sold 3 of a dozen left.

sold any?

eggs more than of a dozen and had How many eggs had she before she

15. What must be paid for 18 boxes of oranges when of a box costs $15?

16. Walter Johnson can make a gate in of a day. How many gates can he make in 6 days?

17. If I add 12 lb. to of my weight it will equal 125 pounds. What is my weight?

18. If I can do a piece of work in 20 days, what part of the work can I do in 3 days?

19. Find the cost of 163 cords of wood at $4.87 a cord.

LESSON 33

1. If I can do a piece of work in 6 days, what part of the work can I do in 60% of a day ?

2. I bought a lot of corn for $400 and sold it at a loss of 5%. Find the loss. Find the selling price.

3. What is the difference between 4. What part of 10¢ is 21¢?

5. If you sell an article for $.12 the gain is what part of the cost?

of $1 and of $5?

that cost you $.10, What per cent?

6. If .12 of the cost of a coat is $33, what is the cost

of the coat?

7. A man had $25. He paid of it for a hat and $12 for a coat. How much money had he left?

8. At $a yard, how many yards of satin will $9 buy? $63?

9. If 43 lb. of tea cost $3.15, how much will 32 lb. cost?

10. At $2 a day, how much will a boy earn in the month of August, provided the first day of August comes on Wednesday?

11. A grocer bought 40 bu. of potatoes, but 4 bushels were damaged. What part of them were bad? What

per cent?

12. A lady had 36 doz. eggs and sold of them at 15¢ a dozen. How much did she receive for what she sold?

13. A man bought a pair of horses for $250 and sold them so as to gain 5% of the cost. Find the gain.

14. A is 45° 30' east of B. at A, what time is it at B? time is it at A?

When it is 10 o'clock A.M.

When it is 4 P.M. at B, what

15. If of a pound of coffee is worth $, how many pounds can be bought for $4.50?

16. How many yards of lace at $2 a yard can be bought for $13.50?

17. If 13 lb. of spice cost 30, how much will 43 lb. cost?

18. What is the interest of $50 for 1 yr. at 8%? What is the interest for 9 mo. at 4%?

19. What is the interest of $200 for 1 yr. at 6%? What is the interest for 6 mo.? For 1 mo.? For 15 da.? For

AREAS

LESSON 34

1. Define surface; polygon; triangle; square; rectangle, rhombus; rhomboid; trapezoid.

Any flat surface which is bounded by four lines or edges is called a Quadrilateral. The square and the rectangle belong to a particular class of quadrilaterals called parallelograms.

2. In what particular respect are a square and a rectangle alike? In what respect are they unlike?

3. In what respect does a rhombus resemble a square? In what respect is it unlike a square?

4. Draw a rectangle 4 in. long and 3 in. wide. Divide it into square inches by drawing lines. Count the square inches, writing inside each square inch its number from one upward.

Write a rule for finding the area of a rectangle.

Show

5. Draw a rhomboid of any convenient size. how it can be changed into a rectangle, keeping the same base and altitude.

Write a rule for finding the area of a rhomboid.

6. Draw a rhombus of any convenient size. Show how it can be changed into a square, keeping the same base and altitude. Write rule for finding the area of a rhombus.

7. Draw a trapezoid of any convenient size. Show how the trapezoid can be changed into a parallelogram, keeping the altitude unchanged. Write rule for finding the area of a trapezoid.

LESSON 35

1. Draw a parallelogram (square, rectangle, rhombus, or rhomboid) of any convenient size. Divide it into two parts by a diagonal, state what figure each part is, and show that the parts are equal.

Give rule for finding the area of a triangle.

A Trapezium is a quadrilateral having none of its sides parallel.

If the trapezium is divided into two parts by the diagonal AC, it will consist of the two triangles ABC and ACD, the diagonal forming the base of both triangles. The altitude of the first

B

TRAPEZIUM

D

triangle is BF and of the second DE. Now, it is evident that the area of the trapezium must equal the sum of the areas of the two triangles.

2. Find the area of a piece of land in the form of a parallelogram, whose length is 30 rd. and altitude 25 rd.

3. The base of a rhombus is 30 yd. and altitude 70 ft. Find its area.

4. Find the area of a trapezoid, one side of which is 12 ft., the other 8 ft., and altitude 4 ft.

5. The base of a rhomboid is 30 ch. and the altitude 25 rd. What is its area?

6. The diagonal of a trapezium is 60 ft., and the altitudes of the triangles into which the trapezium is divided are 40 ft. and 30 ft., respectively. Find the area of the trapezium.

7. Since the area of a parallelogram equals the product of its base and altitude, to what is the base equal? The altitude?

8. The area of a parallelogram whose base is 9 ft. is 54 sq. ft. What is its altitude?

9. The area of a parallelogram is 72 sq. ft. If the altitude is 6 ft., what is the base?

10. Define equilateral triangle; isosceles; scalene.

11. What is the area of a triangle whose base is 1 yd. and altitude 2 ft.?

LESSON 36

A Polygon is generally defined as any flat surface bounded by straight lines; but the name is usually applied to surfaces which are bounded by more than four lines.

If the lines which bound the surface are all equal to one another, the figure is called an equilateral polygon.