What is the surface area of the rectangular pyramid? 10 8 12 15
To calculate the surface area of a rectangular pyramid, you need to calculate the area of the base and the area of the four triangular faces.
The formula for the surface area of a rectangular pyramid is:
Surface Area = Base Area + (1/2 * Perimeter of Base * Slant Height)
In this case, we need to know the dimensions of the rectangular pyramid in order to calculate the surface area. Let's assume the dimensions are:
Length: 10
Width: 8
Height: 12
First, calculate the area of the base:
Base Area = Length * Width
Base Area = 10 * 8
Base Area = 80
Next, calculate the perimeter of the base:
Perimeter of Base = 2(Length + Width)
Perimeter of Base = 2(10 + 8)
Perimeter of Base = 2(18)
Perimeter of Base = 36
Calculate the slant height using the Pythagorean theorem:
Slant Height² = Height² + (1/2 * Base Width)²
Slant Height² = 12² + (1/2 * 8)²
Slant Height² = 144 + (1/2 * 8)²
Slant Height² = 144 + 16
Slant Height² = 160
Slant Height ≈ 12.65
Now, calculate the surface area using the formula:
Surface Area = 80 + (1/2 * 36 * 12.65)
Surface Area = 80 + (1/2 * 36 * 12.65)
Surface Area = 80 + 227.7
Surface Area ≈ 307.7
Therefore, the surface area of the rectangular pyramid is approximately 307.7 square units.