Chapter 12.3, Problem 1CYP

To determine

To find:

The lateral area of a regular hexagonal pyramid.

Answer to Problem 1CYP

The lateral area of the pyramid is $189{\text{ cm}}^2$ .

Explanation of Solution

Given information:

Regular hexagonal pyramid with a base edge of $9$ centimeters and a lateral height of $7$ centimeters.

Calculation:

The lateral area $L$ of a regular pyramid is $L=\frac{1}{2}Pl$ , where $l$ is the slant height and $P$ is the perimeter of the base.

Here, the base is a hexagon of side $9$ centimeters and the slant height is $7$ centimeters.

  $\begin{array}{l}L=\frac{1}{2}Pl\\ =\frac{1}{2}\left(6\cdot 9\right)\left(7\right)\\ =3\cdot 9\cdot 7\\ =189\end{array}$

Hence, the lateral area of the pyramid is $189{\text{ cm}}^2$ .