Find square foot of material needed for tent (Trig)

[ishraqiyun77]

Hi, been a while since I have taken a math class and am missing something on this practice problem. Unfortunately, the text doesn't work it out, so I don't know where I am going wrong. I know if I see it worked out all the way once, it will refresh my memory and I can apply to my actual homework with no issues. It provides the answer, but I am getting different numbers. The green box is the correct answer.

 

[ishraqiyun77]

Disregard. Found this video which explained it.

https://www.youtube.com/watch?v=1-VOduuu2WI

 

[stapel]

Hi, been a while since I have taken a math class and am missing something on this practice problem. Unfortunately, the text doesn't work it out, so I don't know where I am going wrong. I know if I see it worked out all the way once, it will refresh my memory and I can apply to my actual homework with no issues. It provides the answer, but I am getting different numbers. The green box is the correct answer.
View attachment 4877

Not being able to see your work or results, it is not possible to advise you specifically. However, in general, one should note that the total area of fabric will be the sum of the two triangular ends and the two rectangular sides.

Consider the front triangle. This is clearly an equilateral triangle (since it is isosceles with base angles of sixty degrees). The height a = 4. By nature of 30-60-90 triangles (such as that formed by the left side of the triangle, the height line, and the left half of the base), the side length is easily found to be 8/sqrt[3] = (8/3)sqrt[3]. From this, the base length can be found, and thus the area (using the standard formula for the area A of a triangle in terms of its base length b and its height h).

Each rectangle has a length of b = 6 and a "height" equal to a side of the equilateral triangle. Find the area using the standard formula.

From these values, the total face area of the fabric may be found. Note: The question asks for the area of fabric needed to make the tent. This would be an entirely different value, which would take account of wastage, overages for seams, etc.