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]$18 \sqrt{3} \text{ in}$[/tex]
B. [tex]$18 \sqrt{2} \text{ in}$[/tex]
C. [tex]$9 \sqrt{3} \text{ in}$[/tex]
D. [tex]$9 \sqrt{2} \text{ in}$[/tex]
Answer (1)
Recognize that the base is an equilateral triangle with a given side length.
Recall the formula for the height of an equilateral triangle: height = 2 s 3 .
Substitute the side length s = 18 inches into the formula.
Calculate the height: height = 9 3 inches. 9 3 in.
Explanation
Problem Analysis The problem states that the base of a pyramid is an equilateral triangle with a side length of 18 inches. We need to find the height of this equilateral triangle.
Formula To find the height of an equilateral triangle, we can use the formula: height = 2 s 3 , where s is the side length of the equilateral triangle.
Substitution In this case, the side length s is 18 inches. Substituting this value into the formula, we get: height = 2 18 3
Calculation Now, we simplify the expression: height = 9 3 inches Therefore, the height of the triangular base of the pyramid is 9 3 inches.
Examples
Equilateral triangles are not just theoretical concepts; they appear in many real-world applications. For example, architects use them in designing structures for stability, and engineers use them in bridge construction. Knowing how to calculate the height of an equilateral triangle is useful in calculating area and ensuring structural integrity in designs. Consider designing a roof truss system where equilateral triangles provide maximum support with minimal material. The height calculation helps determine the necessary dimensions for the truss.
