< 3. The perimeter of a right-angled triangle is 6 inches. The base is 11 inches and the altitude 2 inches. What is the length of the third side? 4. The perimeter of an isosceles triangle is 15 inches. The base is 3 inches. How long is each of the other sides? 5. The sides of a scalene triangle are 12 inches, 2 inches, and 3 inches. What is its perimeter? 6. A watch charm in the shape of an equilateral triangle requires a gold band 2 inches long to inclose it. What is the length of one side of the charm? 7. How many feet of fencing will enclose an equilateral triangular flower bed, one of whose sides is 4.5 feet? FINDING AREAS OF TRIANGLES A straight line connecting the opposite corners of a quadrilateral is a diagonal. The line AB is a diagonal of figure 1. B FIGURE 1 1. Cut from paper a rectangle whose base is 3 inches and whose altitude is 2 inches. 2. What is the area of this rectangle? 3. Cut along the diagonal. Compare the areas of the two triangles by placing one over the other. 4. The area of each triangle is what part of the area of the rectangle? What is the area of each triangle ? 5. Cut from paper triangles like figure 2 and figure 3. Cut on dotted lines; arrange parts to form rectangles. Show that each triangle is equal to a rectangle whose base is equal to the base of the triangle and whose altitude is one half of the altitude of the triangle. The area of a triangle is equal to one half the product of 16. The base of a right-angled triangle is 8 feet and the altitude is 5 feet. What is the area? 17. The base and altitude of a triangle are each 16 inches. What is the area? 18. What is the area of a triangular lot of land whose base is 20 yards and whose altitude is 25 feet? 19. How many acres in a triangular lot of land whose base and altitude are, respectively, 40 rods and 24 rods? 20. Make up problems in finding areas and perimeters of triangles. DRAWING TO SCALE Written 1. Make a diagram of the top surface of the teacher's desk. Scale": = 1'. 2. Make a diagram of the side of the teacher's desk facing the school, on a scale of " = 1′. 3. Represent on paper the area of the schoolroom floor. Scale 1" = 8'. Compute the number of square feet in the floor. Compute the cost of the floor boards at 6 cents per square foot. 4. Make a diagram of a picture 24" by 20" surrounded by a 2" frame. Scale 1′′ 2′′. = 5. Make a diagram of the door leading from the schoolroom into the hall, on a scale of 1 inch = 1 foot. 6. Make a diagram of the lower sash of one of the schoolroom windows, letting 1 inch represent 6 inches. Compute the area of the lighting surface. 7. Draw a rectangle 2 inches by 1 inches. This figure represents the ground plan of a house drawn on a scale of inch to 4 feet. Find the dimensions of the house and the area covered by the house. 8. Four adjoining house lots are, respectively, 45 ft., 60 ft., 90 ft., and 75 ft. on the street side. Each lot is 120 ft. deep. (a) Draw a diagram of the lots on a scale of 1 inch to 60 feet. (b) Compute the values of the lots at 182 cents per square foot. (c) What is the area of all the lots? (d) What is the perimeter of each lot? 9. In many places building lots are sold by the street frontage. At $22.75 per front foot, what is the value of each lot in problem 8? 10. The diagram of a park covers a space 31" by 5". 1" represents 24 rods. What are the dimensions of the park? Its area in acres? 11. On a scale of " to 1' make a diagram of a floor 16' by 12', and on it a rug 3 yd. by 2 yd. Compute the areas of the floor and of the rug in square feet. 12. Make a diagram of a mirror whose outside dimensions are 32 inches by 20 inches. Scale"=1 foot. 13. Make a drawing of a 2-inch picture frame whose outside dimensions are 32 inches by 24 inches. Scale 1 inch to 8 inches. 14. Find from a geography map the distance from New York to Chicago. From Chicago to St. Louis. From St. Louis to Denver. From Denver to San Francisco. 15. Using some map in your geography, find the dimensions of the state of Colorado. Compute its area in square miles. 16. Find the dimensions and Kansas. Of Utah. Of Nevada. area of Wyoming. Of Of other states. SCALES AND GRAPHS Oral and Written Scales are indicated in various ways, as, for instance: (1) 1′′=3′. This means that a line 1 in. long is used to represent a length of 3 ft. (2). This means that one unit of real length is used to represent four units of real length. given length is used to represent a real length of 5 rd. |