Answered

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The base of a solid oblique pyramid is an equilateral triangle with a base edge length of 18 inches. What is the height of the triangular base of the pyramid?

A. [tex]\( 9 \sqrt{2} \)[/tex] in.
B. [tex]\( 9 \sqrt{3} \)[/tex] in.
C. [tex]\( 18 \sqrt{2} \)[/tex] in.
D. [tex]\( 18 \sqrt{3} \)[/tex] in.

Sagot :

GinnyAnswer
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]
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