Chapter 12.6, Problem 26SR

To determine

Calculate lateral and surface area triangular prism given,

  

Answer to Problem 26SR

Lateral are of triangular prism= $450m^2$

Surface area of triangular prism = $536.602m^2$

Explanation of Solution

Given:

  

Calculations:

Here, we have to calculate lateral and surface area of equilateral triangular prism.

We know that, surface area of triangular prism is the addition of base area and its lateral faces.

  $Surfacearea=2B+ph$

Where, B is the area of triangular base

p is the perimeter of base

h is the height of prism

  $\begin{array}{l}\text{Area of equilateral}\text{triangular }base=\frac{\sqrt{3}}{4}\times sid{e}^2\\ =\frac{\sqrt{3}}{4}\times {10}^2\\ =43.301m^2\end{array}$

Therefore,

  $\begin{array}{l}Surfacearea=2B+ph\\ =\left(2\times 43.301\right)+\left[\left(10+10+10\right)\times 15\right]\\ =86.602+450\\ =536.602m^2\end{array}$

Lateral area is the multiplication of perimeter of base and height of prism.

  $\begin{array}{l}Lateralareaoftriangularprism=perimeter\times height\\ =(10+10+10)\times 15\\ =450m^2\end{array}$

Conclusion:

Therefore, we are able to calculate lateral and surface area of triangular prism using simple formula.