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6. Draw on the blackboard a line 4 feet long. From each end draw lines in the same direction 3 feet in length, making square corners with the 4-foot line. Connect by a straight line the ends of the 3-foot lines.
7. Are the sides of the figure straight? Are the corners equal in size? Find the area of the figure.
8. What is a right angle ? a rectangle ? (p. 112).
9. Show by a diagram the number of square feet in a square yard.
10. Draw a diagram on a scale of 1 inch to 3 feet to represent a rectangle 24 ft. long and 18 ft. wide. Find its area.
Draw diagrams on scales suitable to the size of your tablet or slate and find the surface of each of the following:
11. A rectangle 20 ft. by 24 ft.
15. By actual measurement find the number of square feet in the floor, the door, the blackboard, and the walls of the schoolroom.
16. In what denominations did we find the lengths and widths of the problems just given?
Land is measured in acres, square rods, square feet, etc.
17. Measure a square yard on your playground. How long is it? how wide ?
18. Measure the length and width of your school grounds in rods and feet.
19. Since 163 feet equal 1 rod, how many yards equal 1 rod ? How many square yards equal 1 square rod ?
20. Since 161 feet equal 1 rod, how many square feet equal 1 square rod?
21. A field is 70 rods long and 40 rods wide. square rods are there in it ? how many acres ?
22. Memorize this table :
144 square inches (sq. in.)=1 square foot (sq. ft.)
1 square yard (sq. yd.)
- 1 acre (A.) 640 acres
=1 square mile (sq. mi.) 1 A. = 160 sq. rd. = 4840 sq. yd.= 43,560 sq. ft.
26. 15 A. to sq. rd. 24. 50 sq. ft. to sq. in.
27. 800 sq. yd. to sq. rd. 25. 1600 sq. rd. to A.
28. 54 A. to sq. ft. 29. A farm is 90 rods long and 60 rods wide. Find the number of acres in it. Find its cost at $60 per acre.
30. A lot 100 ft. square has a house 36 ft. by 42 ft. located on it. The remaining space is lawn. Find the number of square feet of lawn. Draw diagram.
31. A concrete sidewalk in front of the lot is 4 ft. wide. Find its cost at 19¢ per square foot.
32. Find the cost of a flagstone walk, 135 ft. long and 6 ft. wide, at 21 per square foot.
. 33. City lots are sometimes sold by the square foot. Find the cost of a lot in Pittsburg 21 ft. by 70 ft. at $27.50 per
34. A farm 160 rods long and 120 rods wide is sold in two pieces, f of it at $60 per acre, and the remainder at $50 per acre. Find the amount of the entire sale. 35. An Iowa farmer owns a farm a mile square.
How many acres has he? Find its value at $85 per acre.
36. A western wheat field 100 rods long and 80 rods wide yields 880 bushels of wheat. Find the average yield per acre.
37. City lots are usually sold by the front foot. Find the cost, at $20 per foot front, of a lot 25 ft. front by 120 ft. deep. Find the cost per square foot.
38. A four-room school building has a slate blackboard 24 ft. by 4 ft. in each room. Find the total cost of the blackboard at 23$ per square foot. 39. The area of a field in the
20 form of a rectangle is 8 acres.
4 If one side is 32 rods, what is
14 the other?
8 These diagrams represent pieces of land. The dimensions are given in 5
4 rods, and the angles are all square.
25 40. Divide the first piece into 3 rectangles and find (1) how many square rods there are in each ; (2) the perimeter of each ; (3) the area of the entire piece in acres.
5 41. Divide the second piece
7 into rectangular lots, and find
13 (1) the perimeter of each;
5 13 (2) the area of each ; (3) the
6 area of the entire piece.
PAINTING AND PLASTERING
Painting, plastering, and kalsomining are generally measured by the square yard. In some localities an allowance is made for doors and windows, but there is no uniform rule in practice.
1. How much will it cost to paint a ceiling 18 ft. long and 15 ft. wide at 10$ per square yard?
2. How much will it cost to kalsomine a hall 30 ft. long, 9 ft. wide, and 15 ft. high, at 5¢ per square yard? (Observe that the perimeter of the hall is 78 ft.)
3. How many square yards of plastering are there in a room 21 ft. long, 18 ft. wide, and 12 ft. high, making no allowance for openings?
4. How much will it cost, at 15$ a square yard, to plaster a room 24 ft. x 193 ft. x 15 ft.?
5. A public hall is 120 ft. x 66 ft. x 224 ft. How much will it cost to paint the walls and ceiling at 10$ per square yard?
THE RIGHT TRIANGLE
· 1. Draw on the blackboard a rectangle 12 inches long and 8 inches wide. Connect the opposite corners by a straight line. This line is called the diagonal of the rectangle.
Into how many parts have we divided the rectangle? Shade one of the parts with chalk. How many angles are there in each part? how many right angles ?
A triangle is a surface having three sides and three angles.
A right triangle is a triangle having one right angle.
The base of a triangle is the side on which it is assumed to stand.
The altitude of a triangle is the line that meets the base line at a right angle.
TO THE TEACHER. - As an aid in drawing have each pupil, if possible, get a right triangle as here shown.
3. Point out the base and altitude in the triangles at the right.
4. Fold a rectangular piece of paper, as ABCD, on its diagonal. Observe:
(1) That the rectangle ABCD and the triangle ABD have the same base and altitude.
(2) That the area of the triangle is just 1 the area of the rectangle.
A Base 4 in. B Hence, 1 of 4 x 2 x 1 sq. in. = 4 sq. in.; area.
The area of a right triangle equals the unit of measure multiplied by the product of the base and altitude.
Draw on a scale suitable to your paper and find the area of the following right triangles in square inches :
5. Base 10 in., altitude 8 in. 7. Base 25 in., altitude 18 in. 6. Base 12 in., altitude 6 in. 8. Base 36 in., altitude 24 in.
9. Find the area of a field in the form of a right triangle whose base is 80 rods and altitude 40 rods.