Question

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? 9√2 in. 9√3 in. 18√2 in. 18√3 in. 18 in.

Explanation:

Step1: Recall equilateral triangle height formula

For an equilateral triangle with side length \( s \), the height \( h \) can be found using the Pythagorean theorem. If we split the equilateral triangle into two right triangles, the hypotenuse is \( s \), one leg is \( \frac{s}{2} \), and the other leg is \( h \). So \( h = \sqrt{s^2 - (\frac{s}{2})^2} \).

Step2: Substitute \( s = 18 \) inches

Substitute \( s = 18 \) into the formula: \( h = \sqrt{18^2 - (\frac{18}{2})^2} = \sqrt{324 - 81} = \sqrt{243} \).

Step3: Simplify the square root

Simplify \( \sqrt{243} \). Since \( 243 = 81\times3 \), \( \sqrt{243} = \sqrt{81\times3} = 9\sqrt{3} \).

Answer:

\( 9\sqrt{3} \) in. (Option: \( 9\sqrt{3} \) in.)