How much fabric is needed to make a tent in the shape of a triangular prism with the following measures?

273 ft 2
329 ft 2
294 ft 2
266 ft 2

300 ft^2

Step-by-step explanation:

The total area will be some sum of areas of rectangles and triangles. The area of a rectangle is the product of its length and width:

A = LW

The area of a triangle is half the product of its base length and height:

A = (1/2)bh

If we assume the dimensions shown on the diagram are supposed to be feet, rather than yards, the areas can be added up as follows:

left side flap: (8 ft)·(12 ft) = 96 ft^2

right side flap: (5 ft)·(12 ft) = 60 ft^2

Then the area of the two side flaps togther is ...

left flap area + right flap area = (96 +60) ft^2 = 156 ft^2

The bottom area is ... (9 ft)·(12 ft) = 108 ft^2

The area of each triangular end is ..

end area = (1/2)(9 ft)(4 ft) = 18 ft^2

so the two of them together total 2·(18 ft^2) = 36 ft^2.

Then the sum of areas for the side flaps, bottom, and triangular ends is ...

(156 + 108 + 36) ft^2 = 300 ft^2

Comment on the question

We cannot find any combination of these areas that will add to give any of the offered answers. We believe this question should be regarded as a waste of time, badlly edited and not checked by its publisher. Unfortunately, there are all too many of those in published curriculum today. You have every right to be confused by it.

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