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ACT Math 5.5 Plane Geometry 600 Views


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Description:

ACT Math: Plane Geometry Drill 5, Problem 5. How much material do you need to cover the entire tent?

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Transcript

00:02

Here's your shmoop du jour, brought to you by Outward Bound. Don't worry—we won't

00:07

throw you to the wolves.

00:09

It is your first day of Outward Bound and you need to pitch a tent in the form of a

00:12

triangular prism with the dimensions shown.

00:16

How much material do you need to cover the entire tent?

00:20

And here are your potential options...

00:25

Since we're trying to find the amount of material needed to cover the tent, we need

00:28

to find the surface area.

00:30

First, we need to find the area of each individual shape

00:33

in the triangular prism and then... add them all up.

00:37

Let's start with the triangles that make up the front and back of the tent.

00:41

They have a height of 5, and a base length of 24

00:44

We can plug in these values to get the area of each triangle, which turns out to be 60

00:51

square feet. There are two of these in the tent, so they

00:54

have a total surface area of 120 square feet. As for the two remaining rectangles,

00:58

we have a length of 40 feet, and a width of 13 feet; by calculating the area of each,

01:06

we get 520 square feet. Again, we have two of these, so we have to

01:10

multiply it by 2 to get 1040 square feet. We have to add the areas of the triangles

01:16

and the rectangles to get our total surface area, and when we do that, we get 1,160 square

01:22

feet of material needed. Option D is just right.

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