The surface area of a triangular prism can be calculated using the following formula:
Surface Area = (Base Perimeter x Height) + (2 x Base Area)
To break this down further, the formula consists of two main components:
- Base Perimeter: This is the total length of all three sides of the triangular base. If you denote the lengths of the base sides as a, b, and c, the perimeter can be calculated as follows:
- Base Perimeter = a + b + c
- Base Area: This is the area of the triangular base, which can be calculated using the formula:
- If you know the base b and height h of the triangle, use:
- Base Area = (1/2) * b * h
- For other methods, you can use Heron’s formula if you know the side lengths:
- Calculate the semi-perimeter, s = (a+b+c)/2
- Then, the area can be found using:
- Base Area = √(s(s-a)(s-b)(s-c))
Finally, once both the Base Perimeter and Base Area have been determined, plug those values into the surface area formula.
For example, if you have a triangular prism where the base sides are 3, 4, and 5 units, and the height of the prism is 10 units:
- Base Perimeter = 3 + 4 + 5 = 12 units
- Assuming we’re using the base side of 4 as the base and a height of 3:
- Base Area = (1/2) * 4 * 3 = 6 square units
Plug these into the surface area formula:
- Surface Area = (12 x 10) + (2 x 6)
- Surface Area = 120 + 12 = 132 square units
Thus, the surface area of the triangular prism is 132 square units.