The amount of nylon that Tina needs to make the tent she designed is [tex]122\: \rm ft^3[/tex]
How to form mathematical expression from the given description?
You can represent the unknown amounts by the use of variables. Follow whatever the description is and convert it one by one mathematically. For example if it is asked to increase some item by 4 , then you can add 4 in that item to increase it by 4. If something is for example, doubled, then you can multiply that thing by 2 and so on methods can be used to convert description to mathematical expressions.
For this case, we need to form an expression for the amount of nylon that will be used (assuming no overlap or openings are there).
Amount of nylon used = Surface area of the tent(outer or inner, both are same)
S = Surface area of tent = surface area of faces that make it up = 3 rectangles and 2 triangles.
Both 2 non-bottom rectangles are of same measure, but bottom one is different, and both 2 triangles are of same measure.
Let we have:
- R = area of a rectangular face(non-bottom) of tent
- B =area of the bottom rectangle that makes up the tent
- T = area of a triangular face of tent
Then, we get:
[tex]S = 2R +B+ 2T[/tex]
Now, each non-bottom rectangle is 5 ft long, 7 ft wide, thus:
[tex]R = \rm Length \times width = 5 \times 7 = 35 \: \rm ft^2[/tex]
The bottom rectangle has 4 ft length and 7 ft width, thus:
[tex]B = 4 \times 7 = 28 \: \rm ft^2[/tex]
Each triangle is 6 feet high and has 4 ft of base.
[tex]T = \dfrac{1}{2} \times \rm base \times height = \dfrac{1}{2} \times 4 \times 6 = 12 \: \rm ft^2[/tex]
Thus, we get:
[tex]S = 2(35) + 28 + 2(12) = 122 \: \rm ft^3[/tex]
Thus, the amount of nylon that Tina needs to make the tent she designed is [tex]122\: \rm ft^3[/tex]
Learn more about surface area here:
https://brainly.com/question/11938672
