Plan the solution, but do not solve: 1. The cyclometer of a bicycle reads at the close of each day as follows: Monday, 841.62 mi.; Tuesday, 873.84 mi.; Wednesday, 910.05 mi.; Thursday, 919.42 mi.; find the average daily ride. 2. On Monday morning a cistern contained 627.5 gal. of water. Tuesday it rained and 127.46 gal. ran into the cistern; Thursday it rained and 472.01 gal. ran into the cistern; the following Monday morning there were 710.91 gal. of water in the cistern; find the average daily consumption of water. 3. In 1900, 2,895,661 dozen pairs of leather gloves and mittens were made in the United States; how many pairs was this per inhabitant, the population being 76,303,387? 4. The number of men's gloves and mittens was .783 of the total number; the number of women's gloves, .112; of boys', .085; and girls', .02; find the number of each. 5. The distance from Cincinnati to St. Louis is 341 mi.; how long will it take a train to make the run, if it goes at the rate of 28.3 mi. per hour the first three hours, 26 mi. the next 2.7 hours, and 30.7 mi. the remainder of the time? 6. By density of population is meant the average number of inhabitants per square mile. For Massachusetts the density is 348.9. The land area is 8,040 sq. mi.; find the population of Massachusetts. 7. The population of Mississippi is 1,551,220; its density of population is 33.5; find its land area. 8. The population of Wisconsin is 2,069,042; its land area is 54,450; find its density of population. 9. Two steamers left New York for Liverpool at 10 a. M., Saturday. The average speed of the first was 386.4 mi. per day; of the second, 495.35 mi.; how far apart were they by 10 P. M., Wednesday? PROBLEMS-COMMERCIAL PRODUCTS 155 1. The following numbers express approximately in millions of dollars the value of the gold produced by the leading sources in 1901: Alaska...... 63. | California..... 16. Arizona.... 4. Colorado...... 27. Montana........ 4.75. 6.5. These values are more easily compared if they are represented by parallel rectangles. Thus: Draw the same set of rectangles on the blackboard, using 1 inch for each division of the scale. The following tables show the States or Territories of the United States which lead in the production of various commercial articles, and the approximate amounts produced recently: Draw a set of rectangles to represent the numbers in each. of the above tables. FORM STUDY AND MEASUREMENT Trapezoids 1. Which are the parallel sides in the figure? What is the altitude of the triangle ABC? Of triangle ADC? A D Why are they equal? A four-sided figure having one and only one pair of opposite sides parallel is B called a trapezoid. 2. How is the area of triangle ABC found? Of triangle ADC? 3. Compare the area of the trapezoid with the sum of the areas of the triangles. 4.h times the lower base+h times the upper base is the same ash times the lower base+ the upper base; how may the area of the trapezoid be found? 15 ft. 5. Find the area of the trapezoid in the figure. The number of square units of area in a trapezoid is one-half the product of the number of units in the altitude and in the sum of the lengths of the bases. 20 ft. 5 ft. 6. Let s represent the sum of the two parallel sides of a trapezoid and a its altitude; what stands for its area? Find the areas of the following trapezoids: FORM STUDY-TRAPEZOIDS 157 1. A field is in the form of a trapezoid. The parallel sides are 116 yd. and 84 yd. and the distance between them is 50 yd.; how much will it cost to plow it and sow it with wheat at 6¢ per 10 square yards? 2. What will the stone for the wall in the figure cost at 974 per square foot of the face? 3. The board supporting the end of a wagon seat is in the form of a trapezoid; how many square inches are there in such a board 14 in. wide at the top, 20 in. wide at the bottom, and 10 in. high? 4 FT 4. The sail of a ship is 40 ft. wide at the bottom, 30 ft. at the top, and 30 ft. high; how many square yards are there in it? 5. A railway is surveyed across a lot 400 yd. square. The strip of land is 10 yd. wide, and has one side along the diagonal; its parallel sides are 566 yd. and 546 yd. in length. At 324 per square foot, what is the cost of the land taken? What is the area of each part left? Find the unknown parts in the following: 10. What is the area of a trapezoid of bases 8 in. and 6 in. and of altitude 4 in. ? 158 PROBLEMS-AREAS 1. How many triangles are visible in the roof of the building shown in the picture? 3. Each of the triangles on the end at the right has an altitude of 20 ft. and a base of 8 ft.; find the area of this part of the roof. Find the areas of the squares in the second story just beneath these triangles. 4. Each side of the shade in the picture is 3 in. wide at the top, 6 in. wide at the bottom, and 9 in. high; how many square inches of material are there in one side? In the whole lamp-shade? 5. The glass faces of a street-lamp are trapezoids. The top is a 6-in. square, the base is an 8-in. square, and the middle frame is a 12-in. square. The altitude of each upper trapezoid is 9 in., and of each lower one 17 in. How many square inches of glass are there in the lamp? The 6. The four sides of a cake tin are trapezoids. dimensions of the bottom are 4 in. by 8 in. and of the top are 6 in. by 10 in. The depth down each side is 3 inches. How many square inches of metal are there in the whole tin? |