Please help with this tent problem so i can understand fro step to step?

Question

A two-person tent is to be made so that the height at the center is a = 4 feet (see the figure below). If the sides of the tent are to meet the ground at an angle α = 60°, and the tent is to be b = 10 feet in length, how many square feet of material will be needed to make the tent? (Assume that the tent has a floor and is closed at both ends, and give your answer in exact form.)

Answer 1

The tent consists of  two isosceles triangles of height 4 ft. with base angles of 60 deg,

If each half of the base of a triangle measures x ft., then:

4 / x = tan(60) = sqrt(3)

x = 4 / sqrt(3)

x = 4 sqrt(3) / 3.

The area of each triangular end is:

A1 = 4x

= 16 sqrt(3) / 3 ft^2.

If s ft. is the length of each sloping side of the isosceles triangles, then:

4 / s = sin(60)

s = 4 / sin(60)

8 / sqrt(3)

= 8 sqrt(3) / 3.

Each sloping side of the tent has area:

A2 = 8 sqrt(3) * 10 / 3

= 80 sqrt(3) / 3 ft^2.

The base of the tent has area:

A3 = 2x * 10

= 80 sqrt(3) / 3 ft^2.

The total area is:

2(A1 + A2) + A3

= [ 2(16 + 80) + 80 ] sqrt(3) / 3

= 272 sqrt(3) / 3 ft^2.