Answer:
The tarp needed to complete your tent = 93.67 ft².
Step-by-step 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) = [tex]\sqrt{4^2+2^2} =\sqrt{16+4}= \sqrt{20} =\sqrt{4*5} =2\sqrt{5}[/tex]
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.
