Question

Find the surface area of the figure below. Use the Pythagorean Theorem to find theslant height.Round to the hundredths (2 decimal places) if necessary.

Answer 1

ANSWER

$864\text{ cm}^2$

EXPLANATION

To find the surface area of the triangular pyramid given, apply the formula:

$A=\text{ Base Area}+\frac{1}{2}(\text{ Perimeter }*\text{ Slant Height})$

First, we have to find the slant height of the pyramid by applying Pythagoras theorem:

$l^2=12^2+(\frac{18}{2})^2$

where l represents the slant height.

Solve for l in the equation above:

$\begin{gathered} l^2=144+81=225 \\ \\ l=\sqrt{225} \\ \\ l=15\text{ cm} \end{gathered}$

Now, find the surface area of the pyramid:

$\begin{gathered} A=(18*18)+\frac{1}{2}((4*18)*15) \\ \\ A=324+\frac{1}{2}(72*15) \\ \\ A=324+540 \\ \\ A=864\text{ cm}^2 \end{gathered}$

That is the answer.