Question

How much material is needed to construct a triangular tent that is 6 feet wide 4 feet tall and 8 feet long with side measurements of 5 feet?

Answer 1

Answer: 152ft^2

The amount of material needed to construct the tent is 152ft^2

Step-by-step explanation:

The amount of material needed to construct a triangular tent= the surface area of the triangular tent.

S.A = area of the 2 side rectangles + area of the 2 side triangles + area of the base.

S.A = Ab + At + Ar ....1

Area of the base Ab= Length × width = 8×6 = 48ft^2

Area of the two triangles At = 2 × 0.5 × width × height

At = width × height = 6×4 = 24ft^2

Area of the two rectangles Ar = 2 × side measurement × length

Side measurement is given as 5ft.

or it can be calculated using;

Side length can be calculated using Pythagoras theorem.

Examining the figure attached, we can see that;

Side breadth b = √(h^2 + (w/2)^2)

b = √(4^2 + (6/2)^2) = √(16+9) = √25

b = 5ft

Ar = 2×5×8 = 80ft^2

From eqn1, S.A can be solved as;

S.A = 48 + 24 + 80

S.A = 152ft^2