Chapter SH, Problem 12.7.1EP

To determine

To find: the lateral area and surface area of pyramid

Answer to Problem 12.7.1EP

The lateral area and surface area are $46.8i{n}^2,62.4i{n}^2$ .

Explanation of Solution

Given:

Formula used:

Lateral area of the pyramid is $L=\frac{1}{2}PI$

Total surface area of the prism is $S=L+B$

Lateral area of the pyramid is

  $L=\frac{1}{2}PI$

Here $P$ is the base perimeter and $I$ is the slant height.

Total surface area of the prism is

  $S=L+B$

Here $B$ is the area of base.

Perimeter of the base is

  $P=6+6+6\to P=18$

Slant height is $I=5.2in.$

Here base is an equilateral triangle.

Area of the base is $\frac{\sqrt{3}}{4}{\left(side\right)}^2$ .

  $\begin{array}{l}B=\frac{\sqrt{3}}{4}{\left(side\right)}^2\\ =\frac{\sqrt{3}}{4}\times 6^2\\ =9\sqrt{3}\end{array}$

Lateral area is

  $\begin{array}{l}L=\frac{1}{2}PI\\ =\frac{1}{2}\times 18\times 5.2\\ =46.8\end{array}$

Surface area is

  $\begin{array}{l}S=L+B\\ =46.8+9\sqrt{3}\\ \approx 62.4\end{array}$

Hence, the lateral area and surface area are $46.8i{n}^2,62.4i{n}^2$ .

Conclusion:

Hence, the lateral area and surface area are $46.8i{n}^2,62.4i{n}^2$ .