How to Find the Lateral Area of a Triangular Prism

To find the lateral area of a triangular prism, you need to focus on the sides of the prism that connect the two triangular bases.

The formula for the lateral area (LA) of a triangular prism is:

LA = perimeter of the base × height of the prism

Here’s how to calculate it step by step:

1. Determine the shape of the triangular base: Identify the triangle’s sides. For a triangle with sides a, b, and c, you will need to find the perimeter.
2. Calculate the perimeter of the triangular base: Add up the lengths of all three sides:

Perimeter (P) = a + b + c

3. Measure the height of the prism: This is the distance between the two triangular bases.
4. Plug the values into the formula: Multiply the perimeter of the triangular base by the height of the prism to find the lateral area:

LA = P × height

For example, if the sides of the triangular base measure 3 cm, 4 cm, and 5 cm, and the height of the prism is 10 cm:

1. Calculate the perimeter: P = 3 + 4 + 5 = 12 cm
2. Then, apply the formula: LA = 12 cm × 10 cm = 120 cm²

So, the lateral area of the triangular prism would be 120 square centimeters.