3. Compare the base and altitude of the rhombus ABCD with the base of the square, ABEF. 4. Do you see that the area of a rhombus is equal to that of a rectangle having the same base and altitude? 5. Make a drawing and see if the same rule is true of a rhomboid. 6. Give the name of the figure ABCD. 7. Cut out of paper a trapezoid four times as c large as this figure. parallel edges will coincide. Place the two pieces so that 8. Fold so that the two Crease and cut on the crease. what were the two parallel sides shall form one continuous side. See EFGD. What form have you now? 9. The base of this rectangle is the sum of what two sides of the trapezoid? 10. The altitude of the rectangle is what part of the altitude of the trapezoid? Learn To find the area of a trapezoid multiply the sum of the two parallel sides by of the altitude. Find the area of trapezoids of the following dimensions: Radius Diameter Circumference 1. The line that bounds this circle is called its 2. The straight line that passes through the center touching both sides is the 3. What is the radius? 4. The circumference of every circle is how many times its diameter? 5. This ratio is usually expressed by the Greek letter (pi). 3.1416. = 6. How do you find the circumference when you know the diameter? 7. How do you find the diameter when you know the circumference? 9. Arrange the parts as shown in Fig. 2. Is the area of Fig. 2 the same as that of Fig. 1? 10. What is approximately the shape of Fig. 2? How do you find its area? Learn To find the area of a circle multiply one half of the circumference by the radius. 11. What dimensions of a circle do you need to know to find its area? If only one dimension is given how do you find the other? Find the area of a circle when the: 12. Diameter is 17.5 ft. 14. Circumference is 50 in. 15. Circumference is 5 ft. 4 in. 16. Radius is 20 rd. 13. Radius is 41 ft. 17. Diameter is 28 ft. 1. All kinds of lumber are measured by board feet. 2. According to size and use pieces of lumber are called boards, planks, scantlings, joists, plates, girders, beams, etc. 3. A board foot is equivalent to a square piece of board 1' long, 1' wide, and 1" thick. Boards less than 1" in thickness are reckoned as one inch. 4. Find the number of board feet in a plank 18' by 9' by 3". 9 18' X 12 × 3 = If the plank was 1" thick, each foot in length would contain of a board foot. Then 18' would contain 18 X 12; and since it is 3" thick it will contain (18 X 12 X 3) board feet. Use cancelation. NOTE: - When boards are 1 in. thick the number of board feet in a board is the same as the square feet of one side. 5. How many feet of lumber are required for a tight board fence 140 ft. long and 5 ft. high? 6. If each plank is 2 in. thick, how many feet of lumber will be needed for a floor 12' by 16'? 7. One end of a barn measures 40 ft. in width and 20 ft. to the eaves, and the altitude of the gable is 15 ft. How many feet of lumber will cover this end? 8. If each side of the roof measures 80 ft. by 25 ft., find the number of feet of boards that will cover the roof. 9. If the floor is covered with 3-in. planks find the cost of the floor at $18 per M. 10. Find the cost of 15 joists, each 20′ × 9′′ × 6′′, at $1.85 per C. 11. How many board feet are there in 8 sticks of timber 18′ x 10" × 12"? 12. At $16.73 per M, find the cost of 35 planks, each 24′ × 16′′ × 3". 13. How many boards 12 ft. long will it take to enclose a square field 48 rd. on a side, with a fence 5 boards high? 14. If each board is 6 in. wide, find the cost of the boards at $15 per M. 1. This diagram represents a room 18 ft. long, 10 ft. wide. How many breadths of carpeting 1 yard wide will be needed? How long will each breadth be if there is a loss of 6 in. on each breadth for matching? How many yards of carpet will it take for Learn: Divide the width of the room by the width of the carpet to find the number of breadths when the carpet runs lengthwise. Add the loss in matching to the length of the room, to find the length of each breadth. Multiply the length of each breadth by the number of breadths to find the amount of carpet needed. 2. How would you find the number of breadths needed when the carpet runs widthwise? 3. A room is 18 ft. by 24 ft. The carpet is of a yard wide and runs lengthwise. If there is a waste of 9 in. on each breadth for matching, how many yards of carpet will it take for the room? At $1.25 a yard, find the cost of the carpet. When the breadths run lengthwise, find the cost of carpeting from the following data: 1. American wall paper is usually 11⁄2 ft. wide and 24 ft. long for a single roll and 48 ft. long for a double roll. A fraction of a roll is not sold and unless otherwise stated the price of a single roll is given. It is not easy to estimate exactly the amount of paper needed for a room, especially since paper hangers do not always use the same rule. The following rule is sufficiently accurate for all purposes: Find the number of feet in the perimeter of the room, leaving out the widths of the doors and windows. Divide by 11⁄2 feet (the width of the paper), to find the number of strips required. Divide the length of a roll by the height of the room, to find the number of strips in a roll. Divide the strips needed for the room by the strips in a roll, to find the rolls required. In the first and third divisions, if there is a fraction take the next higher integer; in the second division take the next lower integer. 2. A hall is 18 ft. by 6 ft. and 7 ft. high. There is one door and one window, each 3 feet wide. At 24 a roll, find the cost of the paper. NOTE 2 (18 ft.+63 ft.) = 49 ft. perimeter. = 42 ft. 42 ft. ÷ 11⁄2 ft. = 28. No. of strips for room. 28 strips = 3 strips = 93.. 10 rolls for room. 24 x 10 = $2.40. When the ceiling is to be papered find the quantity needed in the same way. Find the cost of papering, including the ceiling: |