Question

What is the formula for the surface area of a triangular prism.

Answer 1

Hint: A prism consists of bases and sides.
For finding the surface area of the triangular prism we need to add the surface area of their bases and sides.
A Triangular prism consists of five sides. They are three rectangular sides and two triangular sides.
The triangular prism looks like this:

Complete step by step solution:
Let us consider that,
h is the height of the triangular base.
b is the base of the triangular base.
l is the length of the rectangular side.
s is the width of the one side of the triangular base.
The surface area of the prism is:
$\Rightarrow {{S}_{prism}}={{S}_{bases}}+{{S}_{sides}}$
The bases are triangles.
Area of each triangle becomes:
$\Rightarrow {{A}_{triangle}}=\dfrac{1}{2}bh$, where b is the base and h is the height of the triangle.
$\Rightarrow {{A}_{onebase}}=\dfrac{1}{2}bh$
$\Rightarrow {{A}_{bothbase}}=2\left( \dfrac{1}{2}bh \right)=bh$
$\Rightarrow {{S}_{bases}}=bh$
The sides are rectangles.
We are having three rectangles.one rectangle with length l and breadth b and two rectangles with length l and breadth s.
$\Rightarrow {{A}_{onerec\tan gle}}=lb$
$\Rightarrow {{A}_{anotherrec\tan gle}}=ls$
$\Rightarrow {{A}_{allrec\tan gle}}=lb+ls+ls$
$\Rightarrow {{S}_{sides}}=lb+2ls$
$\Rightarrow {{S}_{prism}}={{S}_{bases}}+{{S}_{sides}}$
$\Rightarrow {{S}_{prism}}=lb+bh+2ls$

Therefore, the formula for the surface area of a triangular prism is \[bh+lb+2ls\].

Note: students must know the concept of surface area. Students must know the basic formulas of areas like area of triangle and rectangle. Students must know the basic knowledge of triangular prisms. Students should also know the volume of the triangular prism is the multiplication of the area of the triangle with the height that is $v=\dfrac{1}{2}\times h\times s\times l$ .