![]() We can divide this rectangle into two congruent triangles (Figure 9.22). Figure 9.21 The area of a rectangle is the base, b, b, times the height, h. In the rectangle in Figure 9.20, we’ve labeled the length b b and the width h, h, so it’s area is b h. We can use this fact to help us visualize the formula for the area of a triangle. We now know how to find the area of a rectangle. The length is 14 feet and the width is 12 feet. The formula for the perimeter of a rectangle relates all the information. The width is two feet less that the length, so we let L − 2 = width Since the width is defined in terms of the length, we let L = length. Now we can draw a figure using these expressions for the length and width. The width of a rectangle is two inches less than the length. Figure 9.20 The area of this rectangular rug is 6 6 square feet, its length times its width. Since A = 2 ⋅ 3, A = 2 ⋅ 3, we see that the area, A, A, is the length, L, L, times the width, W, W, so the area of a rectangle is A = L ⋅ W. What about the area of a rectangle? Remember the rectangular rug from the beginning of this section. P = L + W + L + W or P = 2 L + 2 W P = L + W + L + W or P = 2 L + 2 W If you started at one corner and walked around the rectangle, you would walk L + W + L + W L + W + L + W units, or two lengths and two widths. The perimeter, P, P, of the rectangle is the distance around the rectangle. The sides are labeled L for length and W for width. Figure 9.19 A rectangle has four sides, and four right angles. We refer to one side of the rectangle as the length, L ,Figure 9.19. The opposite sides of a rectangle are the same length. Figure 9.17 A cube that measures 3 inches on each side is made up of 27 one-inch cubes, or 27 cubic inches.Ī rectangle has four sides and four right angles. So each little cube has a volume of 1 1 cubic inch, and the volume of the big cube is 27 27 cubic inches. How many little cubes does it contain? If we were to take the big cube apart, we would find 27 27 little cubes, with each one measuring one inch on all sides. Suppose the cube in Figure 9.17 measures 3 3 inches on each side and is cut on the lines shown. ![]() ![]() Figure 9.16 Cubic measures have sides that are 1 unit in length. A cubic centimeter is a cube that measures one centimeter on each side, while a cubic inch is a cube that measures one inch on each side (Figure 9.16). We often use cubic centimeters, cubic inches, and cubic feet. When measuring the volume of a rectangular solid, you measure how many cubes fill the container. Volume is measured in cubic units such as cubic inches or cubic centimeters. When you measure how much it takes to fill a container, such as the amount of gasoline that can fit in a tank, or the amount of medicine in a syringe, you are measuring volume. Figure 9.15 The rug contains six squares of 1 square foot each, so the total area of the rug is 6 square feet. Each square is 1 1 foot wide by 1 1 foot long, or 1 1 square foot. Figure 9.14 Square measures have sides that are each 1 1 unit in length.įigure 9.15 shows a rectangular rug that is 2 2 feet long by 3 3 feet wide. A square inch is a square that is one inch on each side (Figure 9.14). A square centimeter is a square that is one centimeter (cm) on each side. We often use square inches, square feet, square centimeters, or square miles to measure area. ![]() When you want to know how much tile is needed to cover a floor, or the size of a wall to be painted, you need to know the area, a measure of the region needed to cover a surface. Figure 9.13 This tape measure measures inches along the top and centimeters along the bottom. Inch, foot, yard, mile, centimeter and meter are units of linear measure. A tape measure might remind you of a line-you use it for linear measure, which measures length. When you measure your height or the length of a garden hose, you use a ruler or tape measure (Figure 9.13). Understand Linear, Square, and Cubic Measure
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