10.1.2 Surface Area of Pyramids and Cones (continued)
The lateral and surface area of a right pyramid are determined in this example. The figure is given as a square pyramid with base edge length 4 inches and slant height 10 inches. To calculate the lateral surface area, substitute the known values into the formula for lateral surface area. The lateral surface area is 80 in 2 . To calculate the surface area of the pyramid, substitute the known values into the formula for surface area. The area of the base is the square of the edge length because the base is a square. The surface area is 96 in 2 . The lateral and surface area of a regular right pyramid are determined in this example. The figure is given as a hexagonal pyramid with base edge length 2 meters and slant height 8 meters. To calculate the lateral surface area, substitute the known values into the formula for lateral surface area. The lateral surface area is 48 m 2 . To calculate the surface area of the pyramid, substitute the known values into the formula for surface area. The area of the base is one half the product of the apothem and the perimeter. The apothem is determined by recognizing that it is the long leg of a 30°-60°-90° right triangle whose short leg has length 1 m. The length of the apothem is 3. The surface area is 48 6 3m . 2 +
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