Chapter 12.6, Problem 28SR

To determine

Calculate lateral and surface area triangular prism given,

Answer to Problem 28SR

Lateral are of triangular prism= $104m^2$

Surface area of triangular prism = $152m^2$

Explanation of Solution

Given:

Calculations:

Here, we have to calculate lateral and surface area of 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

  $\begin{array}{l}\text{Area of triangular }base=\frac{1}{2}\times base\times height\\ =\frac{1}{2}\times 8\times 6\\ =24m^2\end{array}$

Therefore,

  $\begin{array}{l}Surfacearea=2B+ph\\ =\left(2\times 24\right)+\left[\left(8+6+10\right)\times 9\right]\\ =48+104\\ =152m^2\end{array}$

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

  $\begin{array}{l}Lateralareaoftriangularprism=perimeter\times height\\ =(8+6+10)\times 9\\ =104m^2\end{array}$

Conclusion:

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