1. How do you find the area of a rectangle? 2. How many square inches are there on the surface of a 6-in. cube? 3. How many 4-in. squares can be cut from a 20-in. square? 4. If the area of a rectangular field is 77 sq. rd., and the base is 11 rods, what is the altitude? 5. How many square rods are there in a field 80 rd. long and 40 rd. wide? How many acres are there? 6. How many cubic feet are there in a cord of wood? 7. What are the dimensions of a cord of wood? 8. A pile of wood is 32 ft. long, 4 ft. high, and 4 ft. wide. Find the number of cords in the pile without finding the number of cubic feet. 9. A block of granite is 4 ft. long, 3 ft. wide, and 2.5 ft. thick. How many cubic feet does it contain? 10. At $1.25 a cubic foot find the cost of the granite block in the eleventh example. 11. How many square yards are there in a ceiling 18 ft. by 24 ft? At 20 a square yard, find the cost of painting the ceiling. 12. How many cubic feet are there in a rectangular block 2 ft. square at the end and 6 ft. long? 13. How many times larger would a block be that was twice as long, twice as wide, and twice as thick? 14. How many blocks of an inch on a side can be sawed from a 2-in. cube? 15. How many square rods are there in a rectangular garden, 8 rd. long and 5 rd. wide? 16. What is this garden worth at $2 a square rod? 17. What will it cost to fence this garden at $1.25 a rod? 18. Give the area of a rectangle measuring 71⁄2 inches by 6 inches. In estimating the cost of painting or plastering in most places it is the custom to deduct from the total area one half of the area of the openings. Since this rule varies, you should be guided by the custom observed in your locality. 1. This diagram represents the walls, ceiling, and floor; 16' long 12' wide, 9' high. There are 2 doors, 2 × (6 sq. ft. × 4) = 48 sq. ft. in windows. 5 sq. ft. x 5 = 43 sq. ft. x 1 = 43 sq. ft. in baseboard. (56+48 +25) + 43 sq. ft. 107 sq. ft. to be deducted. 696 sq. ft. 696 sq. ft. 107 sq. ft. = 588 sq. ft. of plastering. 2. At 20 a square yard find the cost of plastering a room 20' long, 17' wide, and 12′ high. There are 4 doors each 7' by 41, 3 windows each 6′ by 41', and a baseboard 8 in. high. 3. A room is 18' by 24' by 9'. There are 2 doors 4' by 71, 2 windows, 4' by 6', and a baseboard 9 in. high. Find the cost at 22 a square yard of plastering the room. 4. Find the cost at 2 a square yard of kalsomining the walls and ceiling of a room 16' by 15' by 10', when no allowance is made for openings. 1. How many degrees are there in a circle? 2. What part of the whole circle does it take to measure the angle in Fig. 1? 3. Then Fig. 1 is an angle of how many degrees? 4. It is also called a right angle. 5. An angle is the difference in direction of two straight lines that meet or would meet if produced. 6. An acute angle is an angle smaller than a right angle. Which figure is an acute angle? 7. An obtuse angle is an angle greater than a right angle. Which figure is an obtuse angle? 8. A triangle is a plane figure bounded by three straight lines. 9. Triangles are named from their largest angles, as acute triangle, right triangle, and obtuse triangle. Name the triangles at the top of the page. 10. Angles are measured by means of a protractor, which is half a circle, whose circumference is marked off into degrees. 11. Cut from cardboard a protractor and use it in measuring all the angles on this page. TABLE OF ANGLES AND CIRCLES 60 seconds (") = 1 minute (') 12. Any part of the circumference of a circle is an arc. One quarter of the circumference is a quadrant. 1. Triangles are also named from their sides as, equilateral, isosceles, and scalene. 2. An equilateral triangle has 3 equal sides. An isosceles triangle has 2 equal sides. A scalene triangle has none of its sides equal. Fig. I A Fig. 2 Fig. 3 3. The base of a triangle is the side upon which it rests. 4. The vertex is the angle opposite the base. 5. The altitude is the perpendicular distance from the base, or the base produced, to the vertex. 6. From Fig. 3, can you see that the area of a triangle is equal to the area of a rectangle having the same dimensions? 7. From Fig. 1 and 2, can you see that the area of a triangle is equal to the area of a rectangle having the same base and of the altitude? Learn: The area of a triangle is equal to half the area of a rectangle having the same base and altitude. Find the area of triangles with the following bases and altitudes: 8. 36 ft., 24 ft. 10. 17 yd., 15 yd. 12. 19 rd., 13 rd. 9. 2'6", 3'. 11. 3 yd. 1 ft., 4 ft. 13. 7 ft. 8 in., 5 ft. 2 in. 14. State a rule for finding the base when the area and altitude are given, also for finding the altitude when the area and base are given. 1. A plane figure bounded by straight lines is a polygon, meaning many angles. 2. A quadrilateral is a polygon of 4 sides. 3. You will seldom use any polygon except the triangle and quadrilateral. It may be well to know that a figure of 5 sides is a pentagon; of 6 sides, a hexagon; of 8 sides, an octagon; of 9 sides, a nonagon; of 10 sides, a decagon. 4. The quadrilaterals are: The square, having 4 right angles and 4 equal sides. The oblong, having 4 right angles, and opposite sides equal. Squares and oblongs are also called rectangles. The rhombus, having no right angles, but all its sides equal. The rhomboid, having no right angles, and only opposite sides equal. The trapezoid, having only two of its opposite sides parallel. The trapezium, having none of its sides parallel. Fig. 1. Fig. 2 Fig. 3 Fig. 4 Fig. 5 Fig. 6 5. Name each of these figures. 6. State the rule for finding the area of a rectangle. 7. State the rule for finding one dimension when the area and the other dimension are given. 3 8. What will be the cost of paving and curbing a street of a mile long and 42 ft. wide, if the paving costs $1.25 a square yard, and the curbing costs 45g a linear foot? 9. A house is 32 ft. long and its rafters are 15 ft. long. Find the total weight of snow on this roof, if the weight on each square foot is 17 lb. 10. Measure the size of all the windows and find the amount of lighting surface in the room. |