8. A kitchen is 9 feet long and 8 feet wide. How much will the linoleum cost to cover this floor at $2.25 per square yard? 9. The area of a rectangle is 208 square inches. It is 16 inches long. How wide is it? Suggestion: How many inch squares are there in one row along the length? Since the whole rectangle contains 208 inch squares, how many rows of squares are there? 10. The sidewalk in front of a city residence is 4 feet wide. If the lot has a frontage of 45 feet, how much did the walk cost at $1.50 per square yard? 11. A tennis court is 78 feet long and 36 feet wide. How many square feet of space are used in laying out a tennis court? An acre contains 43,560 square feet. What decimal part of an acre is the area of the tennis court? 12. The area of a rectangle is 48 square feet. The length is 8 feet. What is the width? 13. A yield of 899 bushels, of corn was obtained from a field 60 rods long and 36 rods wide. What was the average yield per acre from this field? Exercise 3. Parallelograms Parallel Lines Two straight lines are parallel if they are the same distance apart throughout their length. The above figures show three pairs of parallel lines drawn in different positions. Parallel lines will not meet, however far they may be extended. ALTITUDE 1. How are the opposite sides of this parallelogram drawn? A parallelogram is a foursided figure with two pairs of parallel sides. Any side of a parallelogram may be considered as the base. The lower side is indicated as the base of the parallelogram in the figure shown above. 2. What kind of angles does the dotted line make with the base? This dotted line is called the altitude and represents the distance between the base and the opposite side. BASE Area of a Parallelogram Cut a parallelogram out of a piece of tablet paper. Fold part of the base over on itself and crease a line for the altitude. Cut or tear the parallelogram along this altitude into two parts. Show how these two parts can be arranged to form a rectangle. How does the base of the rectangle compare with the base of the parallelogram? Note that the creased line is the altitude of both the parallelogram and the rectangle. The area of the rectangle is equal to the product of its base and altitude. The area, the base and the altitude of the parallelogram are each equal to the area, base and altitude of the rectangle. Thus we can see that: The area of a parallelogram is equal to the product of its base and altitude. A rectangle is also a parallelogram. The figure shown above is sometimes called a rhomboid to distinguish it from a rectangle or oblong. A rhomboid with equal sides is also called a rhombus. Exercise 4 1. Find the area of a parallelogram with a base of 11 inches and an altitude of 81 inches. 2. What is the area of a parallelogram with a base of 13 feet and an altitude of 13 feet? 3. A truck garden in the shape of a parallelogram has a base of 24 rods and an altitude of 15 rods. How many acres are there in the garden? 4. A diagonal road, 2 rods wide, runs across a man's farm. The road measures 85 rods in length. How many acres does this road take 40 RD out of the farm? 20 RD 85 RD. Suggestion: The length may be taken as the base of the parallelogram thus formed and the altitude as the width of the road. 5. How many acres are there in the field at the left of the road with the dimensions as shown in the illustration? 6. A flower bed in the shape of a parallelogram has a base of 3 yards and an altitude of 7 feet. Find the area of the flower bed in square feet. 7. A board in the shape of a parallelogram is 6 feet long and 8 inches wide. How many square feet are there in the area of one side? 8. A field in the shape of a parallelogram is 30 rods long and 16 rods wide. How much is the field worth at $150 an acre? 9. A field in the shape of a parallelogram is 16 rods long and 12 rods wide. Find its area in acres. BASE The two parallel sides are called the bases of the trapezoid, and the distance between them the altitude. The altitude must make what kind of angles with the base? Area of a Trapezoid Draw a trapezoid on paper and cut it out. Make a second trapezoid exactly the same size as the first, using the first as a pattern. Arrange the second trapezoid in the position shown by the dotted lines. What shaped figure is formed? 1. How long is the base of this parallelogram? The altitude of the parallelogram is the same as the altitude of the trapezoid. The area of the parallelogram is equal to the sum of the two bases of the trapezoid multiplied by the altitude. The trapezoid is what part of the area of the parallelogram? Show then that the following statement is true: The area of a trapezoid is equal to į the sum of the two bases multiplied by the altitude. 1One-half the sum of the two bases may be called the average base. 2. Find the area of a trapezoid with two bases equal to 7 inches and 15 inches and an altitude of 6 inches. Solution: 7 inches + 15 inches=22 inches. 1 of 22 inches=11 inches, the average base. 11X6=66. Therefore the area of the trapezoid=66 square inches. 3. What is the area of a trapezoid with bases of 40 rods and 20 rods and an altitude of 30 rods? Find the areas of the trapezoids having the following Altitude 4. 15 inches. 21 inches. 16 inches. 5. 40 rods. 45 rods. 32 rods. 6. 10 feet. 16 feet. 11 feet. 7. is feet. 21 feet. { feet. 8. 92 inches. 13 inches. 9] inches. 9. 327 rods. 482 rods. 40 rods. 10. [ feet. 13 feet. feet. 11. 8 rods. 42 rods. 40 rods. ) 32 RD 10 RD 30 RD. 12. A railroad cuts a field into two trapezoids with di mensions as shown in the dia- gram. Find the area of each 13. A board 12 feet long is 8 18 RD. inches wide at one end and 12 inches wide at the other. Find the number of square inches in the area of the board. 14. Bring to the class problems which are based upon the measurements of fields or other objects in your community that have the shape of a trapezoid. 24 RD |