17. Divide 25 cu. ft. 1200 cu. in. into three equal parts. 19. Divide 42 cu. ft. 1500 cu. in. into six equal parts. Statutory weights. The practice of selling farm and garden produce by the bushel is becoming less common, and instead there is a growing tendency to sell such commodities by weight. The weights per bushel of these commodities are fixed by law in the different states, and are known as statutory weights. A few of these weights, together with the exceptions in certain of the states, are shown in the following table: 1. Find the value in Texas of 2500 lb. of oats at 40¢ per bushel. 2. Find the value of the oats in Ex. 1 if they are held at the same price in New Jersey; in Maryland. 3. Find the value in New York of 15,250 lb. of potatoes at $1.12 per bushel; of 25,400 lb. of potatoes at $1.04 per bushel. 4. Find the values in Ex. 3 if the potatoes are held in Virginia. What is the difference in values between the two states? 5. Find the total value of the following: 1260 lb. of wheat at $1.20 per bushel 6. Find the total value of the following: 245 lb. of clover seed at $5.00 per bushel 960 lb. of clover seed at $4.75 per bushel 1550 lb. of clover seed at $4.25 per bushel RECTILINEAR PLANE FIGURES Angle. An angle is a figure formed by two straight lines which meet in a point. The figure at the right shows an angle which is designated by the letters A, B, and C, or the number 1 placed within the angle. The angle is read: "the angle ABC," or "the angle 1." The point B where the lines meet is called the vertex of the angle, and the lines BA and BC the sides of the angle. B A Right angle. If one line cuts another so as to make four equal angles, the angles formed are X called right angles. The lines are then said to be perpendicular to each other. A -B Y In the figure at the right, the angles XOA, AOY, YOB, and BOX are right angles, since the four angles are equal. Degree. The angle which is equivalent to one ninetieth of a right angle is taken as the unit of measure of angles. This unit is called a degree (1°). There are 90° in a right angle and 360° in the sum of all the angles about a point, such as the point O in the figure above. Plane surface. The top surface of a school desk, the surface of the blackboard, or the surface of still water are examples of a plane surface or a plane. In each case there is measurable length and breadth, but no thickness. Plane figure. A plane figure is a figure all of whose lines lie in the same plane surface. A figure drawn on the blackboard is a good illustration of a plane figure. Triangle. A triangle is a closed plane figure which is bounded by three straight lines. A triangle, therefore, has three sides and three angles. The sum of the three angles of a triangle is shown in geometry to be 180°. Right triangle. A right triangle is a triangle which has a right angle, that is, an angle of 90°. The side opposite the right angle is called the hypotenuse. TRIANGLE Hypotenuse RIGHT TRIANGLE Rectangle. A rectangle is a four-sided closed plane figure whose sides are straight lines and whose angles are right angles. Square. A square is a rectangle all of whose sides are equal. RECTANGLE 90 SQUARE Perimeter. The perimeter of a closed plane figure is the sum of the lengths of the lines which form it; that is, it is the distance around the figure. EXERCISES 1. The sides of a triangle are 3 ft. 2 in., 4 ft. 8 in., and 4 ft. 9 in. Find the perimeter of the triangle. 2. Each of the three sides of a triangle is 2 ft. 7 in. Find the perimeter of the triangle. 3. Find the perimeter of a square 2 ft. 4 in. on a side. 4. The adjoining sides of a rectangular field are 40 rd. 2 ft. and 20 rd. 11 ft. respectively. Find the perimeter of the field. The opposite sides of a rectangle are equal. 5. Measure the length and width of your classroom and find the perimeter of the room. 6. How much picture molding must be used to go once around a room 16 ft. 6 in. by 20 ft. 9 in. ? 7. How much molding is required in making frames for ten pictures each 18 in. by 22 in.? 8. How much barbed wire is needed to fence in two rectangular fields with a four-strand fence if one of the fields is 250 ft. by 350 ft. and the other is 640 ft. by 1200 ft. ? 9. How many pounds of wire are needed in Ex. 8 if the wire runs 16 ft. to the pound? What is the total cost of the wire at $5.50 per hundredweight? Area of a square. A square which is 1 in. on a side is said to have an area of 1 sq. in. (1 square inch); a square which is 1 ft. on a side an area of 1 sq. ft.; and so on. 7 The square inch, square foot, square yard, and so on are the units of area, according as the figures considered are measured in inches, feet, or yards. 6 5 3 1 If one of the small squares in the figure at the right represents 1 sq. in., 2 it is readily seen by counting that a square 2 in. on a side contains 4 small squares, or 4 sq. in.; a square 3 in. on a side has an area of 9 sq. in.; and so on. The area of a square in square units is equal to the number of units in its side times the number of units in its side. This statement may be shortened as follows: Area of a square = (number of units in side) × (number of units in side) square units. If it is understood that A shall stand for area in square units" and for "number of units in its side," the above expression may be still further shortened by writing A = s3, in which s2 means 8 × 8. Since, if the units in s are inches, the area is in square inches, if 8 is in feet, the area is in square feet, and so on, there can be no misunderstanding of what A represents. Such a method of expressing a rule is called a formula, and is easier to remember than a rule. In applying a formula to a problem it is necessary to substitute values for the letters, compute the result, and assign to it its proper denomination. EXAMPLE. Find the area of a square which is 9 in. on a side. Since s is a dimension in inches, A is in square inches, and hence the area of the square is 81 sq. in. Area of a rectangle. In the figure below, if each small square represents 1 sq. in., it is readily seen by counting that rectangle A, which is 4 in. long and 2 in. wide, contains 8 small squares, or 8 9 8 7 6 5 B 4 D 2 1 units in length," and w for "number of units in width," the above rule may be written as a formula as follows: A = lw, in which it is understood that the writing of 7 and w without any sign means that their product is to be taken. |