10.1.1 Surface Area of Prisms and Cylinders (continued)
The lateral and surface area of a right prism are determined in this example. The length and width of the base and the height of the prism are given. To find the lateral area of the right prism, first calculate the perimeter of the base using the given values for length and width. The perimeter of the base is equal to 16 cm. Substitute the perimeter of the base and the height of the prism into the formula for the lateral area. The lateral area is found to be 160 cm 2 . To find the surface area of the right prism, calculate the area of the base by multiplying the given length and width. The area of the base is equal to 15 cm 2 . To find the surface area of the prism, substitute the lateral area and base area into the formula for surface area. The surface area is 190 cm 2 . The lateral and surface area of a right prism are determined in this example. The length of an edge of the base and the height of the prism are given. To find the lateral area of the right prism, calculate the perimeter of the base using the given value for the length of an edge of the base. The perimeter of the base is 48 cm. Substitute the perimeter of the base and the height of the prism into the formula for the lateral area of the prism. The lateral area is 576 cm 2 . To find the surface area of the right prism, calculate the area of the base. The formula for the area of the base is B = (1/2) aP , where a is the length of the apothem. The base is a hexagon, so the perimeter is 8(6) = 48 cm long. The apothem is the longer leg of a 30°-60°-90° right triangle with short leg length of 4. Substitute the values of the base area and the lateral area into the formula for surface area to find the surface area approximately equal to 908.6 cm 2 .
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