12. The perimeter of a square is 12 yards. What is the area in square feet? 13. A rectangular lot is 50 ft. by 75 ft. The house on the lot is 25 ft. by 50 ft. How many square feet are there in the yard? 14. How many square inches are there in the surface of a common brick, which is 8 inches long, 4 inches wide, and 2 inches thick? 15. A farmer wishes to make a grain bin 8 ft. long, 5 How many square feet of boards In one end? In one side? ft. wide, and 4 ft. deep. will he have in the bottom? This figure is drawn to a scale of 12 ft. to 1 inch. 349. To find the area of the entire figure we divide it into four rectangles and find the area of each separately. 1. What is the length of A? The width? The area in square feet? In square yards? 2. Find the area of B in square feet. In square yards. 3. What is the area of C? The area of D? 4. Find the area of the entire figure in square yards. 5. How does the area of A compare with that of C? 6. A is what part of D? D is what part of B? 7. What part of the entire figure is B? What part is D)? 8. Copy the figure, omitting the dotted lines. Make other dotted lines dividing the figure into 3 rectangles. Find the area of each rectangle. 350. Draw a rectangle 4 in. long and 3 in. wide, and divide it into square inches. How many sq. in. have you? Draw another rectangle 6 in. long and 2 in. wide. Is its area equal to that of the first rectangle? Has it the same dimensions (length and width)? Draw a third rectangle 12 in. long and wide enough to have the same area. What is its width? Draw a rectangle 6 in. by 8 in. Draw another twice as long, but only half as wide. Are their areas equal? Draw another twice as wide as the first, but only half as long. Compare the areas. What may be the dimensions of a rectangle containing 24 sq. ft. 36 sq. ft.? 64 sq. ft.? Complete: A rectangle 6 in. by 3 in. equals another 3 in. by in. ft. in. A rectangle 4 in. by 7 in. is how many times one that is 2 in. by 7 in.? A rectangle that is 6 in. by 5 in. is what part of one that is 9 in. by 5 in. ? How many rectangles each 2 in. by 3 in. are equal to one that is 6 in. by 3 in.? To one 10 in. by 3 in.? A B ALTITUDE D BASE 351. Point out the base of the shaded triangle. The altitude. What part of the rectangle is the triangle? What is the area of the rectangle? What, then, must be the area of the triangle? The area of the rectangle is 3 X 4 sq. units. The area of the triangle is of 3 X 4 sq. units. The area of a triangle is expressed by one-half of the product of the numbers that represent its base and altitude. 1. If the base of a triangle is 6 inches and the altitude 3 inches, what is its area? of (3 X 6) sq. in. = 9 sq. in. Find the area of the following triangles: 2. Altitude 8 inches, base 6 inches. 5. Cubic Measure. 352. Cubic Measure is used in measuring solids. 1728 cubic inches (cu. in.) = 1 cubic foot (cu. ft.). = 1 cubic yard (cu. yd.). 27 cubic feet A solid that is 1 foot long, 1 foot wide, and 1 foot thick is called a cubic foot. Find a block of wood, a stone, or a box that is about as large as a cubic foot. Suppose Fig. 1 is drawn to a scale of 1 inch to 3 feet, or 1 yard. Then OD represents what length? What is the area of each face? a cubic yard? Does the figure represent A solid that is 1 yard long, 1 yard wide, and 1 yard thick is called a cubic yard. FIG. 3. FIG. 2. 354. Fig. 3 represents a cubic foot. If we cut off a piece an inch thick and divide it into inch cubes, how many of them shall we have? How many such pieces can be cut from a cubic foot? Then how many cubic inches in a cubic foot? A cubic yard is 3 ft. long, 3 ft. wide, and 3 ft. thick. Find the value of 3 X3 X 3. Is the product the number of cubic feet in a cubic yard? What are the dimensions of a cubic foot? Find the value of 12 X 12 X 12, and compare it with the number of cubic inches in a cubic foot. Find how many cubic inches in a cube that measures 4 inches on each side. Build the cube with blocks (inch cubes). Volumes. 355. How many faces has a cube? Are they all equal? Is each face a rectangle? Figure 4 represents a solid 6 inches long, 4 inches wide, and 3 inches thick. How many faces has the solid? Is each face a rectangle? A solid bounded by 6 rectangles is called a rectangular solid. In Figure 4 each little cube represents 1 cubic inch. Find how many cubic inches there are. There are three layers, each containing 4 rows of the little cubes, as ABCD. Each row contains 6 little cubes, or cubic inches, hence the 4 rows contain 24 cubic inches. Since there are 24 cu. in. in each layer, in the 3 layers there are 3 X 24 cu. in., or 72 cu. in., which is the volume. Find the value of 6 X 4 X 3. Does the product equal the number of cubic inches in Fig. 4? (6 × 3 × 4) X 1 cu. in. cu. in. = The volume of a rectangular solid is expressed by the |