8. The boys planted to late potatoes a strip 1151 ft. wide the entire length of the field, and planted to sugar beets all the remainder of the piece of land. How many acres did they plant to each of these crops? Complete the plan in Ex. 5 and check the areas of the different strips by adding them together and comparing the result with the number of acres which you have already found in Ex. 1. 9. It takes 7 bu. of seed potatoes to plant an acre. If seed potatoes cost $3.20 per 100 lb., and 1 bu. weighs 60 lb., how much did the boys pay for the seed potatoes needed to plant the strip in Ex. 8? 10. The strip of late potatoes in Ex. 8 yielded 3 pk. to each square rod of land, and the boys sold the potatoes for $1.50 per 100 lb. Taking the weight of 1 bu. as 60 lb., how much did they receive for their crop of potatoes? 11. Land such as was used for the sugar beets in Ex. 8 yields 18 tons per acre, and the crop is worth $10 per ton. The expenses per acre of raising sugar beets are as follows: rent, $10; seed, 12 lb. at 70¢ per pound; labor, $21. Find the profit the boys made on their crop of beets. 12. The farmer whose land adjoined the field the boys rented was careless. He planted 82 acres of corn without giving the seed an ear-to-ear test, the result being that four ears out of every bushel of seed corn failed to grow. If we estimate 100 ears of seed corn to a bushel, and the yield at 50 bu. to the acre, what was the farmer's loss at $1.25 per bushel, from failing to test the seed? 13. In Ex. 12, if the total work of testing the seed corn would have required 7 da., what wages per day would the increased yield of corn have paid the farmer? CHAPTER IV I. PRACTICAL MEASUREMENTS Common Plane Figures. We are already familiar with many of the plane figures that we commonly measure. We shall now review these and shall learn how to measure others. Triangle Quadrilateral Rectangle Square Triangle. A plane figure which is bounded by three straight lines is called a triangle. Quadrilateral. A plane figure which is bounded by four straight lines is called a quadrilateral. Rectangle. A quadrilateral all the angles of which are right angles is called a rectangle. If necessary the teacher should explain the meaning of right angle, referring to the illustration and definitions on page 114. Square. A rectangle all the sides of which are equal is called a square. Polygon. A plane figure which is bounded by straight lines is called a polygon. The teacher should draw on the blackboard polygons of various shapes. As a preliminary to this chapter the tables on pages 106-114 should be reviewed; and in order that this review shall be thorough, much oral work is provided on pages 202 and 203. REVIEW OF THE TABLES All work oral 1. Express as miles: 320 rd., 640 rd., 1280 rd. 5. Express as cubic yards: 27 cu. ft., 54 cu. ft. 10. How many cubic inches in 1 cu. ft.? in 10 cu. ft.? 15. How many quarts in a barrel of 311⁄2 gal.? 16. How many quarts in a 60-gallon hogshead ? 17. Express as a fraction of an acre: 80 sq. rd., 40 sq. rd. 18. How many right angles in 270° ? in 180° ? in 360°? 19. How many days from May 23 to June 25? 20. How many days from June 11 to July 17? 21. What part of a 16-carat ring is pure gold? 22. Express 11 yd. as rods; as feet; as inches. 23. Express 30 pt. as quarts; as gills; as gallons. 24. How many feet in 2 rd.? 25. How many feet in 10 rd.? in 2 rd. 10 ft.? in 2 rd. 8 ft.? in 5 rd.? in 2 rd.? in rd.? 7 REVIEW OF THE TABLES Numbers 1 to 6, oral 1. How many acres in a tract of land 10 mi. square? 2. How many days from Jan. 19 to Feb. 19? 3. How many square feet in 10 sq. yd.? in 5 sq. yd.? 4. Using 6 qt. a day, how long will 3 bu. of oats last a horse? 5. What is the perimeter of a square that is 41 ft. on a side? 6. What is the side of a square whose perimeter is 14 ft. 4 in.? 7. Since a gallon contains 231 cu. in., how many gallons in 693 cu. in.? in 1617 cu. in. ? in 2541 cu. in.? 8. How many square feet in a surface having an area of 720 sq. in.? in a surface having an area of 5040 sq. in. ? 9. Express a long ton (2240 lb.) as a short ton and hundredths of a short ton. 10. What is the perimeter of a triangle that is 3 ft. 8 in. on each side? 11. If school closes June 21, how many days from noon of the day that school closes to noon of the Fourth of July? 12. How many quarts will a 10-bushel bin hold? a 15-bushel bin? How many pecks will each bin hold? 13. A man buys a building lot that has a frontage of 2 rd. 8 ft. How many square feet in his sidewalk if it is 5 ft. wide? 14. A cellar 16 ft. by 22 ft. is to be excavated to a depth of 6 ft. How many loads (cubic yards) of earth must be removed? 15. If a man buys 13 T. 1800 lb. of coal, how many pounds does he buy? Express this weight in tons and tenths of a ton. 16. A farmer has 3 A. of celery, and the yield is 1550 doz. heads to the acre. How many heads of celery did he raise? Area of a Rectangle. A school building has an entrance hall 10 ft. long and 4 ft. wide. The floor is made of marble squares 1 ft. on a side. What is the number of squares? There are 10 squares in each row, and there are 4 rows. Hence there are 4 x 10 squares. In the same way we see that the area of the floor is 4 x 10 sq. ft. 40 = sq. ft. The length, 10 ft., and the width, 4 ft., are called the dimensions of the floor. Base and Height. The line on which a figure appears to stand is called the base. The distance from the highest point above the base to the base is called the height or altitude of the figure. Finding the Area of a Rectangle. From the above example and definitions and from page 107 we see that The area of a rectangle is equal to the product of the base and height. Such a rule refers to abstract numbers. We do not multiply 10 ft. by 4 ft., but we say that 4 x 10 = 40, the number of square feet. AREA OF A RECTANGLE Find the areas of the following rectangles, using short methods: The teacher should give plenty of practical work in finding the areas of floors, platforms, desks, the school grounds, the sidewalk, and the like. |