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you build a two-person tent, as shown. How many square feet of material is needed to make the tent, assuming the tent has a floor?​

You Build A Twoperson Tent As Shown How Many Square Feet Of Material Is Needed To Make The Tent Assuming The Tent Has A Floor class=

Sagot :

The material is needed to make the tent, assuming the tent has a floor would be equal to 36/√3.

What is a triangular prism?

Connect three rectangles edge to edge. Now close their triangular mouths from both ends. That shape is called a triangular prism.

Let the tent width be w and the given Length is 6 feet.

[tex]tan\theta = \dfrac{opposite }{adjecent} \\\\tan60 = \dfrac{h}{w/2} \\\\\sqrt{3} = \dfrac{6}{w/2} \\\\\sqrt{3} = \dfrac{12}{w} \\\\w = \dfrac{12}{\sqrt{3} }[/tex]

[tex]sin60 = \dfrac{opposite }{hypotenuse} \\\\sin60 = \dfrac{6}{x}\\\\x = \dfrac{6}{\sqrt{3}/2 }\\\\x = \dfrac{12}{\sqrt{3} }[/tex]

The area of the front tent =

[tex]\dfrac{1}{2} \times base \times height\\\\\dfrac{1}{2} \times w\times h\\\\\\\dfrac{1}{2} \times 12/\sqrt{3} \times 6\\\\\dfrac{36}{\sqrt{3} }[/tex]

The area of the back tent is also the same.

Learn more about triangular prisms here:

https://brainly.com/question/16261758

#SPJ1

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