Question

14 in. You want to wrap a gift shaped like the regular triangular prism shown. How many square inches of wrapping paper do you need to completely cover the prism? 8.7 in. 10 in. (The figure is not to scale.) You need square inches of wr Juan Ponce de Leon and the Fountain of Youth ft.

Answer 1

You know that the gift has a shape of a Regular triangular prism. Then, you need to use the following formula for calculate the surface area of a triangular prism:

`SA=2B+Ph`

Where "B" is the area of the base, "P" is the perimeter of the base and "h" is the height of the prism.

Since the base of the triangular prism is a triangle at it is a regular prism:

`\begin{gathered} B=(bH)/(2) \\ \\ P=3s \end{gathered}`

Where "b" is the length of the base of the triangle, "H" is the height of the triangle and "s" is the length of any side of the triangle.

Then, you can rewrite the formula:

`\begin{gathered} SA=2((bH)/(2))+(3s)h \\ \\ SA=bH+3sh \end{gathered}`

In this case:

`\begin{gathered} b=10in \\ H=8.7in \\ h=14in \end{gathered}`

Then, substituting values into the formula and evaluating, you get:

`\begin{gathered} SA=(10in)(8.7in)+3(10in)(14in) \\ SA=507in^2 \end{gathered}`

The answer is:

`507in^2`