ACT Math 5.5 Plane Geometry
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ACT Math: Plane Geometry Drill 5, Problem 5. How much material do you need to cover the entire tent?
|ACT Math||Plane Geometry|
|ACT Mathematics||Plane Geometry|
|Foreign Language||Arabic Subtitled|
Visualize relationships between two-dimensional and three-dimensional objects
|Plane Geometry||Applications of geometry to three dimensions|
|Product Type||ACT Math|
|Properties, Measurement, and Dimension||Visualize relationships between two-dimensional and three-dimensional objects|
And here are your potential options...
Since we're trying to find the amount of material needed to cover the tent, we need
to find the surface area.
First, we need to find the area of each individual shape
in the triangular prism and then... add them all up.
Let's start with the triangles that make up the front and back of the tent.
They have a height of 5, and a base length of 24
We can plug in these values to get the area of each triangle, which turns out to be 60
square feet. There are two of these in the tent, so they
have a total surface area of 120 square feet. As for the two remaining rectangles,
we have a length of 40 feet, and a width of 13 feet; by calculating the area of each,
we get 520 square feet. Again, we have two of these, so we have to
multiply it by 2 to get 1040 square feet. We have to add the areas of the triangles
and the rectangles to get our total surface area, and when we do that, we get 1,160 square
feet of material needed. Option D is just right.