Surface Area of Rectangular Pyramids Practice
1. Find the surface area of a rectangular pyramid with a base of 6 cm by 8 cm and a height of 10 cm.
The surface area of a rectangular pyramid can be calculated using the formula:
Surface Area = Base Area + (1/2) * Perimeter of Base * Slant Height
First, calculate the base area:
Base Area = length * width
Base Area = 6 cm * 8 cm
Base Area = 48 cm^2
Next, calculate the perimeter of the base:
Perimeter of Base = 2 * (length + width)
Perimeter of Base = 2 * (6 cm + 8 cm)
Perimeter of Base = 2 * 14 cm
Perimeter of Base = 28 cm
Now, calculate the slant height using the Pythagorean theorem:
Slant Height = sqrt(height^2 + (1/4) * perimeter^2)
Slant Height = sqrt(10^2 + (1/4) * 28^2)
Slant Height = sqrt(100 + 196)
Slant Height = sqrt(296)
Slant Height ≈ 17.2 cm
Now, plug in the values into the surface area formula:
Surface Area = 48 cm^2 + (1/2) * 28 cm * 17.2 cm
Surface Area = 48 cm^2 + 14 cm * 17.2 cm
Surface Area = 48 cm^2 + 240.8 cm^2
Surface Area ≈ 288.8 cm^2
Therefore, the surface area of the rectangular pyramid is approximately 288.8 cm^2.