Exercise 92 1. A tennis court is 78 ft. long and 36 ft. wide. Find its area. 2. Four tennis courts are laid out side by side with a strip 10 ft. wide between adjacent courts, and a strip 15 ft. wide at each end. Find the area of the plot of ground used. Make a drawing of the four courts on the scale of 32 ft. to 1 in. 3. A baseball diamond is 90 ft. square. Find its area. This area is what part of an acre? Give the answer as a common fraction in its lowest terms, and as a decimal fraction correct to .001. 4. A owns a corner lot 60 ft. wide and 100 ft. deep. He puts down a concrete sidewalk 5 ft. wide along the two sides next to the street. The outside edge of the walk coincides with the edge of the lot. Find the cost of the sidewalk at 15 cents a square foot. 5. It costs $1.60 a square foot to lay a brick pavement. How much is that a mile for a pavement 9 ft. wide? 6. Find the area of this L-shaped lot. What is it worth at 12¢ a square foot? 120 FIG. 96. 7. A 15-inch square is how many times 15 sq. in.? Draw both on the scale of 5 in. to 1 in. 8. How many tiles 8 in. square will it take to cover a floor 14 ft. wide and 58 ft. long? 9. In making a box a boy cuts a piece of pasteboard in the shape of Figure 97. How many square inches of pasteboard are needed to make the box? FIG. 97. 10. How much pasteboard is needed for a box 10 in. long, 8 in. wide, and 4 in. deep? 11. Find the area of the T-square given in Figure 98. 12. Make a formula for finding the area of the iron plate given in Figure 99. Compute the area if a = 12 in. and b = 13 in. 2 FIG. 98. FIG. 99. 100. Area of a parallelogram. Construct a parallelogram ABCD with its base, b, about 3 in. long, and its altitude a. Construct the altitudes AM and Rectangle AMKD has, then, the same area as the parallelogram ABCD. Rectangle AMKD has the same base, b, and the same altitude, a, as the parallelogram ABCD. The area of the rectangle AMKD=ab. Therefore, the area of the parallelogram ABCD = ab. Rule. The area of a parallelogram equals the product of its base and its altitude. Exercise 93 1. Copy and complete this table, using the formula A = ab to find the area, A, of each parallelogram. 2. Find the area of a parallelogram whose altitude is 2% more than its base, which is 40 ft. 3. Find the area of a parallelogram whose base is 5% more than the altitude, the base being 315 ft. long. 4. A parallelogram has an area of 240 sq. in. Its altitude is 8 in. How long is its base? 5. A parallelogram has the same base as a rectangle whose area is 520 sq. ft. The altitude of the rectangle is 13 ft. and the altitude of the parallelogram is 20 ft. What is the area of the parallelogram? 101. The area of a triangle. Draw a triangle ABC, and its altitude BM. Through B draw a line BH par allel to AC. Through C draw line CH par allel to AB. Cut out the parallelogram ABHC, then cut along the diagonal BC, thus making two triangles. B H Show that these triangles are the same size by fitting them together. If the area of the parallelogram is 6 sq. in., what is the area of triangle ABC? The parallelogram and the triangle have the same base and the same altitude. Since the area of the parallelogram is the product of its base and altitude, we have the Rule. The area of a triangle equals one-half the product of its base and altitude. State this rule as a formula, representing the area of the triangle by T, its base by b, and its altitude by a. 102. The area of a trapezoid. Draw a trapezoid ABCD. Prolong BC and AD, then lay off CE equal to AD and DF equal to BC. Draw EF, thus forming the parallelogram ABEF. Cut out this parallelogram, then cut along CD, and show that the two trapezoids are of the same size by fitting them together. Trapezoid ABCD is what part of the parallelogram ABEF? B C Calling the lower base of the trapezoid, b, the upper base, b', and the altitude a, how long is the base of the parallelogram? Its altitude? The area of the parallelogram is, therefore, a(b+b′). This is stated in the Rule. The area of a trapezoid is one-half the product of the altitude by the sum of the bases. The formula T=a(b+b') is more easily remembered than the rule. Exercise 94 1. Use the formula Tab to find the area, T, of the following triangles whose bases and altitudes are a and b : 2. A railroad cut off a triangular piece of land from a farm. The longest side of the triangle was 24 rods and the distance of that side from the opposite corner was 8 rods. How much was this land worth at $225 an acre? 3. If a half gallon of paint is required to paint a square (that is, a 10-foot square), how much is needed to paint three triangular gables each having a base of 15 ft. and an altitude of 8 ft.? 4. A section of a wall made by a stairway has the shape and dimensions shown in Figure 103. What is the cost of covering it with burlap at 25¢ a square yard? 5. A concrete walk and a porch were laid at 20¢ a square foot. They were of the shape and dimensions given in Figure 104. Find the cost. 6. Construct a figure like Figure 105 and make a formula for finding its area. Find the area if a=10′′ and b=6′′. 7. Make a figure like Figure 106 and make a formula for finding its area. Find the area if a = 12′′ and b=3′′. FIG. 103. FIG. 104. FIG. 105. FIG. 106. 8. Find the number of yards of material 1 yd. wide that must be bought to make 100 pennants of the shape of Figure 107, if a=8 in. and b=18 in. Find the amount of waste if the material is bought all in one strip. 9. The 42 children in the seventh grade wish to make a pennant for each member of the class. The pennant is FIG. 107. FIG. 108. to have the form given in Figure 108. They think that the area of the pennant can be found more easily by first making a formula. Make this formula. |