To find the surface area of a pyramid, you need to add up the areas of all its faces. The formula for finding the surface area of a pyramid depends on the shape of its base. Here are the formulas for some common types of pyramids:
1. Rectangular Pyramid:
Surface Area = Base Area + (0.5 x Perimeter of Base x Slant Height)
2. Square Pyramid:
Surface Area = Base Area + (0.5 x Perimeter of Base x Slant Height)
3. Triangular Pyramid:
Surface Area = Base Area + (0.5 x Perimeter of Base x Slant Height)
The slant height is the distance from the apex (top) of the pyramid to its base along a slanted line.
Example question:
Find the surface area of a rectangular pyramid with a base length of 6 cm, base width of 4 cm, and a slant height of 5 cm.
Solution:
1. Calculate the base area:
Base Area = Length x Width = 6 cm x 4 cm = 24 cm²
2. Calculate the perimeter of the base:
Perimeter of Base = 2 x (Length + Width) = 2 x (6 cm + 4 cm) = 2 x 10 cm = 20 cm
3. Calculate the surface area:
Surface Area = Base Area + (0.5 x Perimeter of Base x Slant Height) = 24 cm² + (0.5 x 20 cm x 5 cm) = 24 cm² + 50 cm² = 74 cm²
Thus, the surface area of the rectangular pyramid is 74 cm².
Surface area of pyramids practice unit eight, lesson four
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