What is the formula for finding the surface area of a regular triangular pyramid?(1 point)

Question

Responses

SA=lw+12w4h2+l2−−−−−−−√+12l4h2+w2−−−−−−−√
cap s cap A is equal to l w plus 1 half w square root of 4 h squared plus l squared end root plus 1 half l square root of 4 h squared plus w squared end root

SA=a2+2aa24+h2−−−−−−√
cap s cap A is equal to A squared plus 2 A square root of the fraction with numerator A squared and denominator 4 plus h squared end root

SA=12ab+3(12lb)
cap s cap A is equal to 1 half A b plus 3 times open paren 1 half pounds close paren

SA=2(wl+lh+hw)

Answer 1

The formula for finding the surface area of a regular triangular pyramid is:

\[ SA = \frac{1}{2} a^2 + \frac{3}{2} a \sqrt{h^2 + \left(\frac{a}{2}\right)^2} \]

Where:

• \( a \) is the length of a side of the triangular base,
• \( h \) is the height of the pyramid from the base to the apex.

If we analyze the provided response options, none of the given formulas exactly matches this standard formula for the surface area of a regular triangular pyramid.

However, if I were to select an option that closely approximates the correct form, I would lean toward the one with the components involving \( a \) and \( h \). The correct formula should explicitly incorporate half the base area and the areas of the triangular faces that lead up to the apex.

If you need further clarification, please provide additional context or options.