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

`864\text{ cm}^2`

Step-by-step explanation

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

`A=\text{ Base Area}+(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+((18)/(2))^2`

where l represents the slant height.

Solve for l in the equation above:

`\begin{gathered} l^2=144+81=225 \\ \\ l=√(225) \\ \\ l=15\text{ cm} \end{gathered}`

Now, find the surface area of the pyramid:

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

That is the answer.