### Video Transcript

Determine the lateral surface area of the given figure.

The lateral surface area of an object is the area of all of the sides of the object except for the
area of the bases. So since this is a triangular prism, the two parallel bases are triangles. So
we’re gonna be finding the area of everything except for those two triangles, which means we’re
finding the area of the three rectangles. Let’s go ahead and add some things to help visualise
where these rectangles are located.

Here we can see we have two triangular bases and then are three rectangles. So the
lateral surface area will be adding the areas of the three rectangles. Let’s go ahead and do
that.
So the area of this rectangle, which is length times width, would be thirty-two
times sixteen.
The area of this rectangle would be thirty-two times thirty.
And the area of the last rectangle would be thirty-two times thirty-four.

Before we begin multiplying, there actually is a formula that we could use to
solve for the lateral surface area of this prism. However, I want us to actually kind of figure it
out ourselves. So notice, each of these areas of the rectangles have thirty-two in them.
So if we will take the thirty-two out,
we would have this. And there’s something special about the thirty-two, and
there’s something special about what’s inside the parentheses. They all had thirty-two because
that is the height of the prism.
And sixteen plus thirty plus thirty-four is actually the perimeter of the
triangles,
which are considered the bases.

So our formula for the lateral surface area of a prism is equal to the perimeter
of the bases 𝑃 times the height of the prism ℎ.
Let’s keep evaluating to get our answer.
Sixteen plus thirty plus thirty-four
is equal to eighty. And now I need to multiply thirty-two times eighty,
which equals two thousand five hundred and sixty.

So the lateral surface area of the given figure is two thousand five hundred and
sixty inches squared.