# Triangular prism calculator

the step-by-step formula for finding the surface area of a triangular prism:

1. Identify the base of the triangular prism. This is the triangle at the bottom of the prism.
2. Find the area of the base by using the formula for the area of a triangle, which is A = (1/2)bh, where b is the base length of the triangle and h is the height of the triangle.
3. Identify the lateral faces of the triangular prism. These are the three rectangular faces that connect the bases of the prism.
4. Find the area of each lateral face by multiplying the length of the side by the height of the triangle. The height of the triangle is the same as the height of the prism.
5. Add up the areas of the base and the lateral faces to find the total surface area of the triangular prism.

Here is an example:

Suppose we have a triangular prism with the following measurements:

1. Base: a right triangle with base 4 cm and height 3 cm
2. Length of each rectangular face: 5 cm
3. Height of the prism: 7 cm
4. To find the surface area of the prism, we can follow these steps:

Identify the base of the triangular prism:

The base is a right triangle with base 4 cm and height 3 cm.

Find the area of the base:

A = (1/2)bh = (1/2)(4 cm)(3 cm) = 6 cm^2
Identify the lateral faces of the triangular prism:

There are three rectangular faces that connect the bases of the prism.

Find the area of each lateral face:

A = lh = (5 cm)(7 cm) = 35 cm^2
Since there are three lateral faces, the total area of the lateral faces is:

3 x 35 cm^2 = 105 cm^2
Add up the areas of the base and the lateral faces to find the total surface area of the triangular prism:

Total surface area = base area + lateral area
= 6 cm^2 + 105 cm^2
= 111 cm^2
Therefore, the surface area of the triangular prism is 111 cm^2.