EXERCISES 1. Find the cost of covering a square 28 in. by 14 in. with gold leaf at 7¢ a square inch. 2. How many square inches are there in 5 sq. yd.? 3. Find the cost of 18 sq. yd. of canvas at 121 a square foot. 4. A garden plot is 9 rd. long by 20 yd. wide. Find the cost of sodding it at 181 a square yard. NOTE.. The rods must be reduced to yards before multiplying; the result after multiplying will be square yards. 5. An athletic field is 36 rd. by 27 rd.; it is surrounded by a tight board fence 12 ft. high. Find the cost of painting the fence, both sides, at 41 a square yard. 6. Find the cost of an inlaid floor 18 ft. by 16 ft. at $2.50 per square foot. 7. How many square yards are there in 16 sq. rd.? NOTE. There are 5 yd. in a rod. A square rod will equal 5 × 5 sq. уd. 8. A road 21 mi. long is to be paved with asphalt. The asphalt is to reach from curb to curb, a distance of one chain. Find the expense of paving at $2.30 per square yard. 9. How many square yards in a square chain? 10. A rectangular garden plot, 51 yd. long by 39 yd. wide, is to be laid out with a gravel walk, as shown in the foregoing diagram, 6 ft. wide. The leveling of the entire plot will cost 34 a square yard; the walk will cost 8 a square yard; the sodding of the four sections will cost 12¢ a square yard; and an iron fence surrounding the garden. will cost 75% a foot. Find the entire expense. Lesson No. 4. Square Rods, Square Chains, and Square Miles TABLE 160 square rods = an acre 10 square chains an acre 640 acres a square mile EXERCISES 1. A field is 80 rd. long by 64 rd. wide. How many acres? 2. A piece of timber land is 20 mi. long by 3 mi. wide. What is it worth at $14.50 an acre? 3. A wheat field is is 24 bu. to the acre. bushel? mi. long and 12 ch. wide; the yield What is the wheat worth at 85¢ a 4. A square mile of land is divided into 40-acre fields, and each field is surrounded by a wire fence. Find the expense of fencing at $1.20 per rod. 5. Some city property is bought for the purpose of making a new street. The street is to be 66 ft. wide, and the two long sides as shown in the diagram measure 180 yd. and 90 yd. respectively. Find the cost of the property at 47 a square foot. Lesson No. 5. Areas of Four-sided Figures, having two Adjacent Right Angles If two adjacent angles of a four-sided figure are right angles, the area of the figure can easily be found without the use of surveyor's instruments or of higher mathematics. Suppose that we desire to find the area in square feet of the figure ABCD. We have already learned how to find the area of the rectangle ACED, which is simply to multi ply the length by the breadth. Now, in the same way we can find the area of the smaller rectangle EDBF shown by the dotted line, and half of this will be the area of the triangle EDB, and the rectangle and triangle together make up the whole figure. NOTE. -If ACD be not a right angle, the area of the figure can still be found, only we shall have two triangular areas to add to the rectangle instead of one. See Lesson No. 9. 1. Find the area in feet of a four-sided figure having three right angles. The length of the longer side is 12 ft. and of the shorter side 9 ft. The breadth is 8 ft. 2. Find the cost of sodding a garden plot of the shape of the figure described above. AB is 60 ft.; CD is 45 ft.; AC is 36 ft. The price to be 20 a square yard. 3. A farm lies between two parallel roads with two corners right angles as in the above diagram. It has a frontage upon one road of 2 mi. and upon the other road of 2 mi. The distance between the roads is 2 mi. How many acres in the farm? 4. A city lot is surrounded by four streets, two of which are parallel and 20 rd. apart. It has a frontage upon one of these streets of 132 yd. and upon the other of 33 yd. A third street is at right angles to these two. Find the value of the lot at $800 an acre. 5. A railway crosses a Minnesota township as shown in the diagram. It enters one mile from one corner and leaves the township two miles from the opposite corner. many acres on each side of the track? How Lesson No. 6. Measurements of Solids and Volumes A rectangular solid is a body bounded by six rectangular surfaces. If all the sides are squares, the body is called a cube. If the sides are each a foot square, the body is called a cubic foot. The volume is expressed by the product of the length, breadth, and height. The three dimensions must be expressed in the same terms before multiplying—that is, they must be all in inches, or in feet, or in yards. 1. What is the volume in cubic feet of a rectangular solid 3 yd. long, 2 ft. wide, and 6 in. high? |