Question

What is the surface area of the triangular prism?

Answer 1

Please see below.

Explanation:

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The triangular prism look like this:

The surface area of this prism consists of:

`S_("Prism")=S_("Bases")+S_("Sides")`

The bases are triangles. The area of each one is:

`A_("Triangle")=1/2bh` where `b` is the base of the triangle and `h` is the height.

`A_("One Base")=1/2bh`

`A_("Both Bases")=2*1/2*bh=bh`

The sides are rectangles. The area of a rectangle is:

`A_("Rectangle")=l*w` where `l` is the length anf `w` is the width.

In the prism, `l` is the height of the prism and `w` is the length of one side of the triangular base and is normally denoted as `s`.

`A_("Side")=ls`

If the triangular base has unequal sides then you calculate the perimeter `(p)` of the triangle and multiply it by the height of the prism to get the area of the sides (lateral surface area).

If the base is an equilateral triangle then all three sides have equal areas and the lateral surface area becomes `=3ls`

`S_("Prism")=bh+pl`

Answer 2

`A = 3ls + sqrt{3}/2 s^2`

Explanation:

I'm only answering because the other, featured answer is incomplete.

The figure fails to recognize `b=s` and `h=\sqrt{3}/2 s` as happens in an equilateral triangle.

The area of the each rectangular face is `ls.`

The area of each triangular end is `sqrt{3}/4 s^2`

So three rectangles and two triangles gives a total surface area `A` of

`A = 3ls + sqrt{3}/2 s^2`