Question

1. a tent manufacturer is designing a two - man a - frame tent.

a. draw a net of the tent including dimensions.
b. what is the minimum amount of canvas needed to cover the top of the tent?
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c. the design calls for a heavy tarp on the bottom of the tent. determine the surface area of the bottom of the tent.
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Explanation:

Step1: Analyze the tent shape

The tent is a triangular - prism - like shape. For part (a), a net would consist of two congruent triangular faces and three rectangular faces. The triangles have base 4 m and height 2.5 m, and the rectangles have dimensions: two with length 3.2 m and width 3 m, and one with length 4 m and width 3 m.

Step2: Calculate the area of the top (part b)

The top of the tent consists of two congruent rectangles. Each rectangle has length \(l = 3.2\) m and width \(w=3\) m. The area of a rectangle is \(A = l\times w\). The total area of the top \(A_{top}=2\times(3.2\times3)\).
\[A_{top}=2\times9.6 = 19.2\space m^{2}\]

Step3: Calculate the area of the bottom (part c)

The bottom of the tent is a rectangle with length \(l = 4\) m and width \(w = 3\) m. The area of a rectangle is \(A=l\times w\). So \(A_{bottom}=4\times3=12\space m^{2}\)

Answer:

a. A net would have two triangles with base 4 m and height 2.5 m, two rectangles with dimensions 3.2 m by 3 m and one rectangle with dimensions 4 m by 3 m. (It's not possible to actually draw in this text - based format, but this describes what it should look like).
b. \(19.2\space m^{2}\)
c. \(12\space m^{2}\)