what is the surface area of a triangular prism? the height is 5.1 the prism length is 30.5 the slant height of the triangle base is 28.4 the base of the triangular prism is 27.9
The surface area of a triangular prism can be calculated using the formula:
Surface Area = 2 * base area of the triangle + base perimeter * height of the prism
First, we need to calculate the base area of the triangle. This can be done using Heron's formula:
s = (27.9 + 27.9 + 28.4) / 2 = 42.1
Base Area = √(42.1 * (42.1 - 27.9) * (42.1 - 27.9) * (42.1 - 28.4)) = 312.91
Next, we calculate the base perimeter:
Base Perimeter = 27.9 + 27.9 + 28.4 = 84.2
Now, we can calculate the surface area of the triangular prism:
Surface Area = 2 * 312.91 + 84.2 * 5.1 = 625.82 + 429.42 = 1055.24
Therefore, the surface area of the triangular prism is 1055.24 square units.