Question

including the bottom what is the minimum number of square feet of canvas needed to create the outside of the tent.

Answer 1

We want to determine the total surface area of the tent. The surface area would be

Area of 2 triangular faces + area of the opposite rectangular faces + area of the rectangular base

Since the triangular face is an isosceles triangle, we it means that the two opposite sides are equal. Thus, the side lengths are 26ft, 26ft and 20ft. We would find the area of the triangular face by applying heron's formula which is expressed as

`\begin{gathered} \text{Area = }\sqrt[\square]{S(S\text{ - a)(s - b)(s - c)}} \\ s\text{ = }\frac{a\text{ + b + c}}{3} \\ a\text{ = 26, b = 26, c = 20} \\ s\text{ = }\frac{26\text{ + 26 + 20}}{3}\text{ = 24} \\ \text{Area = }\sqrt[]{24(24\text{ - 26)(24 - 26)(24 - 20)}}\text{ = }\sqrt[]{24(-\text{ 2)(- 2)(4)}} \\ \text{Area = 19.596} \end{gathered}`

Area of 2 triangular faces = 19.596 x 2 = 39.192

Area of 2 opposite rectangular faces = 2 x 26 x 40 = 2080

Area of rectangular base = 20 x 40 = 800

Total Surface area = 39.192 + 2080 + 800 = 2919.192

Thus, the minimum number of square feet needed is 2919.192 square feet