Question

You have been asked to create a tent for an upcoming trip. The length will be 6ft, the width 4 ft and the height 4ft. Approximately what is the size of tarp needed to complete your tent? (you will include the floor and door.

Answer 1

The tarp needed to complete your tent = 93.67 ft².

Explanation:

See the attached figure.

The tent has a shape of a triangular prism.

The size of tarp needed to complete your tent = total surface area of the triangular prism

The length will be 6ft, the width 4 ft and the height 4ft.

Total surface area of the triangular prism = area of the floor(6 ft by 4 ft) + area of 2 triangles( 4 ft and the height 4ft. ) + area of 2 rectangles (edge by 6 ft)

The edge (the hypotenuse) =
`√(4^2+2^2) =√(16+4)= √(20) =√(4*5) =2√(5)`

Area of the floor = 4 * 6 = 24 ft²

Area of 2 triangles = 2 * (0.5 * width* height) = 2 * 0.5 * 4 * 4 = 16 ft²

Area of 2 sides = 2 * edge * length = 2 * 2√5 * 6 = 24√5 ft²

Total surface area = 24 + 16 + 24√5 = (40 + 24√5) ft²

Expressing as decimal number 40 + 24√5 = 93.67 ft².

so, the tarp needed to complete your tent = 93.67 ft².