Chapter 12.10, Problem 8IP

To determine

Tofind:Thelateral surface area and surface area of the triangular pyramid.

Answer to Problem 8IP

Thelateral surface area and surface area of the triangular pyramid is $72{\text{in}}^2$ and $87.6{\text{in}}^2$ , respectively.

Explanation of Solution

Given information:

The base side length of the triangular pyramid is 6 inches, slant height is 8 inches, and base area is $15\frac{3}{5}{\text{in}}^2$ .

Calculation:

In a triangular pyramid, the lateral surface area is the sum of the surface area of its three sides.

Write the expression to calculate the lateral surface area.

  $L=\frac{3}{2}bh$

Where,

• $b$ is the base side length.
• $h$ is the slant height.

Substitute the values in the above.

  $\begin{array}{c}L=\frac{3}{2}\times 6\times 8\\ =72{\text{in}}^2\end{array}$

Write the expression to calculate the total surface area.

  $S=\text{Lateral}\text{surface}\text{area}+\text{Base}\text{area}$

Substitute the values in the above expression.

  $\begin{array}{c}S=72+15\frac{3}{5}\\ =72+\frac{78}{5}\\ =87.6{\text{in}}^2\end{array}$

Conclusion:

Therefore, the lateral surface area and surface area of the triangular pyramid is $72{\text{in}}^2$ and $87.6{\text{in}}^2$ , respectively.