Surface area of pyramids quick check unit eight lesson four what is the surface area of a square pyramid where the base edge is 8 feet and the slant height is 16 feet
The surface area of a pyramid can be found using the formula:
Surface Area = Base Area + (1/2 × Perimeter of Base × Slant Height)
In the case of a square pyramid, the base is a square, so the Base Area can be found by squaring the length of one of the sides, in this case, the base edge.
Base Area = (Base Edge)^2
Base Area = 8^2 = 64 square feet
Next, we need to find the Perimeter of Base. Since the base is a square, all sides are equal, and the perimeter is the sum of all the sides of the square.
Perimeter of Base = 4 × Base Edge
Perimeter of Base = 4 × 8 = 32 feet
Now, we have all the necessary values to find the Surface Area.
Surface Area = Base Area + (1/2 × Perimeter of Base × Slant Height)
Surface Area = 64 + (1/2 × 32 × 16)
Surface Area = 64 + 256
Surface Area = 320 square feet
Therefore, the surface area of the square pyramid is 320 square feet.