Answered

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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.

Find The Surface Area Of The Figure Below Use The Pythagorean Theorem To Find Theslant HeightRound To The Hundredths 2 Decimal Places If Necessary class=

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ANSWER

[tex]864\text{ cm}^2[/tex]

EXPLANATION

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

[tex]A=\text{ Base Area}+\frac{1}{2}(\text{ Perimeter }*\text{ Slant Height})[/tex]

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

[tex]l^2=12^2+(\frac{18}{2})^2[/tex]

where l represents the slant height.

Solve for l in the equation above:

[tex]\begin{gathered} l^2=144+81=225 \\ \\ l=\sqrt{225} \\ \\ l=15\text{ cm} \end{gathered}[/tex]

Now, find the surface area of the pyramid:

[tex]\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}[/tex]

That is the answer.

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