1. How many square inches in a rectangle 15" by 6"? 2. How many square yards in a piece of canvas 12 yards long and 31 yards wide? 3. What is the area of a surface 3 yards long and 6 feet wide? 4. How long is a garden 4 yards wide, if it contains 60 square yards? 5. A square flower plot contains 36 square feet. What are its dimensions? 6. How many square feet in the top of a desk 4 feet long and 2 feet wide? 7. What is the area in square yards of a floor 12 feet long and 6 feet wide? 8. A square garden contains 81 square feet. How many square yards? 9. How many acres in a lot of land 32 rods long and 5 rods wide? 10. What part of an acre is a lot of land 8 rods by 2 rods? A lot 10 rods by 10 rods? 11. A piece of paper covers 96 square inches. It is 12 inches long. How wide is it? 12. A rectangle 12 feet long is twice as long as it is wide. Find its area. 13. How many rods of fence will inclose a lot 8 rods long and 6 rods wide? 14. What is the perimeter of a lot 8 rods square? The area? NOTE. Much attention should be given to oral analysis of problems by pupils. This requires concentration of attention and a clear conception of the conditions stated. No set form of expression should be required, but the correct use of "if," "since," and "therefore" should be carefully taught. Pupils should be encouraged to be on the alert for short methods of solution, and to solve orally as many of the problems as possible. Find the areas of rectangles of these dimensions: 25. Find the perimeters of the rectangles. 26. What is the area of the top of a table 4 feet 8 inches long and 2 feet 6 inches wide? 27. A rug is 144 inches long. Its width is two thirds of its length. How many square yards does it cover? 28. A lot of land containing 60 square rods cost $1272. How much would an acre cost at this rate? 29. How many acres in a lot of land 80 rods long and 24 rods wide? Note that in the mechanical work we treat the dimen sions as abstract numbers. Find the area in acres of lots of these dimensions: 40. How many rods of fence would be required to inclose each lot? 41. How many acres in a lot 20 rods square? 42. What part of an acre is a lot containing 20 square rods? 43. The perimeter of a square lot is 100 rods. How many acres in the lot? 44. A square lot has an area of 25 square rods. Find the distance around it. 45. A field 80 rods by 45 rods was divided into 5 equal fields. How many acres in each lot? 46. How many acres in a lot one quarter of a mile long and one eighth of a mile wide? How many rods around the lot? 47. A park reservation 68 rods by 40 rods has 26 trees to the acre. How many trees in the reservation? ANGLES The difference in direction between two straight lines that meet is an angle. The meeting point of the two straight lines is the vertex of the angle. The lines are the sides of the angle. B FIGURE 1 FIGURE 2 FIGURE 3 When the sides form a square corner, the angle is a right angle. (Fig. 1.) When the sides form a right angle, they are perpendicular to each other. Thus in figure 1 the vertical line AC and the horizontal line BC are perpendicular to each other. An angle less than a right angle is an acute angle. (Fig. 2.) An angle greater than a right angle is an obtuse angle. (Fig. 3.) QUADRILATERALS A figure bounded by straight lines is a polygon. A polygon of four sides is a quadrilateral. Lines which have the same direction are parallel lines. Quadrilaterals are classified according to their parallel sides: (1) A quadrilateral whose opposite sides are parallel is a parallelogram. (a) A parallelogram whose angles are right angles is a rectangle. (Fig. 1.) FIGURE 1 FIGURE 2 FIGURE 3 FIGURE 4 (b) A parallelogram whose sides are equal and whose angles are right angles is a square. (Fig. 2.) (c) A parallelogram whose angles are oblique, i.e. not right angles, is an oblique-angled parallelogram, or a rhomboid. (Fig. 3.) (d) An oblique-angled parallelogram whose sides are equal is a rhombus. (Fig. 4.) (2) A quadrilateral having two sides parallel is a trapezoid. (Figs. 5 and 6.) (3) A quadrilateral having no two sides parallel is a trapezium. (Figs. 7 and 8.) FINDING AREAS OF PARALLELOGRAMS 1. Cut from paper a parallelogram like this- making base 4 inches and altitude 2 inches. |