1 mi. Example 1. Express 27 rd. 4 yd. 2 ft. as a fraction of Therefore, 27 rd. 4 yd. 2 ft. = 4591 ft. 4591 ft. A mile equals Example 2. Express 2 yd. 2 ft. 8 in. as a decimal of a mile. Step 1. Expressing 2 yd. 2 ft. 8 in. as fraction of 1 mi. gives of 1 mi. 13 Step 2. Reducing 13 to a decimal gives .0197. Reduce : EXERCISE 61 1. 4400 ft. to the decimal of 1 mi. 9. 2.34 in. to the decimal of 1 ft. 10. 3° 15' to the fraction of a right angle. MEASUREMENTS If the length and width of a rectangle are expressed in the same linear unit, the number of corresponding square units in its area is equal to the product of the numbers in its length and width. Review the explanation on page 14. If it is desired to find area in acres, sections, or townships, the area must first be found in other units and then reduced. Why? EXERCISE 62 1. Find the number of acres in the area of a rectangle whose dimensions are 360 ft. and 121 ft. 2. Find the area of a rectangle 1331 ft. by 720 ft. 3. Find, in acres, the area of a rectangular plot of ground 201 yd. by 10 rd. 5 yd. 4. A railway company acquires the right of way through a territory 154 mi. long, and fences in a strip 80 ft. wide. How many acres does it thus inclose, and how much does it pay for the land at $25 an acre? 5. Find the area of a park 396 ft. by 396 ft. Give your answer in acres. 6. How many acres in a rectangular farm 1.5 mi. long by 1 mi. wide? Find the value of the farm at $49 an acre. AREAS OF RECTANGULAR FIGURES EXERCISE 63 1. A room is 40 ft. x 30 ft. x 18 ft. How many square yards in its walls and ceiling? (What are the various areas to be found and the dimensions of each ?) 2. Find the area, in square yards, of the walls and ceil ing of a room 24 ft. x 16 ft. x 12 ft. 3. ABCD is a rectangular plot of ground 400 ft. by 160 ft. On all four sides of it is a road 15 ft. wide. Find the area of the road. B 4. Skirting a rectangular park 600 ft. long by 560 ft. wide is a road 24 ft. wide, on all sides of the park. Find the area of the road. Suppose a fence is built to inclose the road with the park. How many feet of fencing will be required? 5. A rectangular grass plot 252 feet by 180 feet has a walk around it. The width of the walk is 9 feet. How many flags, 9 inches square, will be required to flag the walk? 6. Find the area of each of the following rectangles, in square feet, correct to two decimal figures: (a) 136 feet 8 inches by 115 feet 4 inches. (c) 78 feet 5 inches by 56 feet 6 inches. (g) 223 feet 10 inches by 78 feet. (h) 618 feet 1 inch by 130 feet 7 inches. HINT. Reduce the inches in each example to the fraction of 1 foot. 7. Find the area of the following rectangles, giving the results in square yards, correct to two decimal figures: (a) 84.5 feet by 76.75 feet. (e) 129.55 feet by 79.63 feet. 8. A cornfield is 213 rods long and 96 rods wide. How many bushels of corn will it produce at to an acre? Find the value of the crop at $48 32 bushels per bushel. 9. A city block is 110 yards long by 90 yards wide. How many acres in a park which extends 7 blocks one way and 5 blocks the other way? 10. A street is 1760 yards long and 20 yards wide. How many thousand bricks, 8 inches by 4 inches, will be needed to pave it? 11. How many tiles, 4 inches on a side, will be required to tile a hall 60 feet by 16 feet? 12. A room is 16 ft. x 12 ft. x 10 ft. How many square yards in the four walls of the room? How many square yards in the walls and ceiling? 13. If a hurricane exerts a pressure of 19.47 pounds per square foot, find in tons the total pressure exerted against the side of a building 50 ft. long and 45 ft. high. Land surveyed by the United States Government surveyors is divided into townships and sections. This system is common in most of the region west of the Mississippi River, but is not used at all in some of the older states. A township is a tract of land 6 mi. square, and it is divided into 36 sections, each 1 mi. square. The sections are numbered as shown in Fig. 1, on the next page; and are subdivided into half sections, quarter sections, etc., named by the part of the section in which they are situated. As a section contains 640 acres, the area of subdivisions can easily be computed. A section is subdivided as indicated in Fig. 2. There are two divisions, E. and W. . The E. is divided into two equal squares called N.E. and S.E. . The W. is divided into two equal squares called N.W. ‡ and S.W. These may be again subdivided as shown in the figures below. 1. Draw a figure and locate S. W. of S.E. ; N.W. of S. E.; N.E. of S. W.; S.E. of S. W. 1. 1 2. Locate N.E. of the N.E. ; S.W. of N.E. ‡. |