How to find the lateral area of a triangular prism?
The lateral area for a triangular prism is the sum of areas of its side faces (which are 3 rectangles).
Answer: Lateral surface area of the triangular prism (LSA) = Perimeter of the base × Height of the Prism
Go through the explanation to understand better.
A triangular prism has three rectangular sides. Let us see what are the dimensions of these rectangles.
1) One dimension of each of these rectangles is the same as one of the dimensions of the base triangle.
2) The other dimension of all three rectangles is the same and is equal to the height of the prism.
Let us consider a triangular prism whose height is 'h'. Let us assume that the side lengths of each of the triangular bases be a, b, and c. Then the dimensions of:
- One rectangular face is 'a' and 'h'. Hence its area = ah.
- The second rectangular face is 'b' and 'h'. Hence its area = bh.
- The third rectangular face is 'c' and 'h'. Hence its area = ch.
The lateral area for the triangular prism is the sum of all three areas. Thus, Lateral surface area of triangular prism (LSA) = ah + bh + ch (or) (a + b + c) h.
We know that (a + b + c) is the perimeter of the base (triangle).