Question

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Answer 1

Notice that the pyramid has four triangular sides and a square-shaped base.

To find the height of the triangles, notice that the slant height of the pyramid can be calculated using the Pythagorean Theorem, since it is the hypotenuse of a right triangle formed with the height of the pyramid and half the side of the square. Then, the slant heihgt of the pyramid, is:

`\sqrt[]{3^2+1^2}=\sqrt[]{9+1}=\sqrt[]{10}`

The area of each triangular side is half its base times its height:

`\begin{gathered} A_T=(1)/(2)b* h \\ =(1)/(2)(2)(\sqrt[]{10}) \\ =\sqrt[]{10} \end{gathered}`

The area of the base equals its side squared:

`\begin{gathered} A_S=L^2 \\ =(2)^2 \\ =4 \end{gathered}`

To find the total surface area of the pyramid, add four times the area of a triangular side plus the area of the base:

`\begin{gathered} S=4A_T+A_S \\ =4(\sqrt[]{10})+4 \\ =4\cdot\sqrt[]{10}+4 \end{gathered}`

Use a calculator to find a decimal expression for the total surface area:

`S=16.649\ldots`