To find the height of the triangular base of an equilateral triangle, let's go through the steps clearly.
Given:
- The base edge length of the equilateral triangle is 18 inches.
For an equilateral triangle, the height can be determined using the formula:
[tex]\[
\text{height} = \frac{\sqrt{3}}{2} \times \text{side length}
\][/tex]
Plugging in the given side length:
[tex]\[
\text{height} = \frac{\sqrt{3}}{2} \times 18
\][/tex]
This simplifies to:
[tex]\[
\text{height} = 9 \sqrt{3}
\][/tex]
So, the height of the triangular base of the pyramid is [tex]\(9 \sqrt{3}\)[/tex] inches.
Thus, the correct answer is:
[tex]\[
9 \sqrt{3} \text{ in.}
\][/tex]
