Surface Area of Triangular Prisms Practice Complete this assessment to review what you've learned. It will not count toward your grade. 5 of 5 Items Question
5
Find the surface area of the triangular prism below.
Base: Equilateral triangle with side length 6 cm
Height of the prism: 8 cm
Remember that the formula for the surface area of a triangular prism is SA = 2B + Ph, where B is the area of the base, P is the perimeter of the base, and h is the height of the prism.
First, calculate the area of the equilateral triangle base:
Area = (sqrt(3) / 4) * side^2
Area = (sqrt(3) / 4) * 6^2
Area = (sqrt(3) / 4) * 36
Area = (sqrt(3) / 4) * 36
Area = 9sqrt(3) cm^2
Then, calculate the perimeter of the base:
Perimeter = 3 * side
Perimeter = 3 * 6
Perimeter = 18 cm
Now, use the formula for the surface area of the triangular prism:
SA = 2B + Ph
SA = 2(9sqrt(3)) + 18(8)
SA = 18sqrt(3) + 144
SA ≈ 192.9 cm^2
Therefore, the surface area of the triangular prism is approximately 192.9 square centimeters.