The material needed to make the tent assumes the shape of a triangular prism and the surface area of the material needed is 193.18 ft².
What is the surface area of a triangular prism?
A triangular prism is indeed a three-sided prism made up of a triangle base, a translational copy, and triple faces connecting equivalent sides in geometry.
The properties of a triangular prism include:
- It has five faces
- It has six edges
- It has nine vertices
Let's assume that the shape of the canvas tents is in form of a triangular prism, to determine the material needed to make the tent, we need to understand the surface area of a triangular prism.
However, let's assume that:
- Each of the three bases of the triangular prism = 6
- The height of the triangular prism = 9
From the image attached below: the surface area of the triangular prism can be calculated by using the following formula:
[tex]\mathbf{A = 2A_B +(a+b+c)h }[/tex]
[tex]\mathbf{A_B = \sqrt{s(s-a)(s-b)(s-c)}}[/tex]
[tex]\mathbf{s = \dfrac{a+b+c}{2}}[/tex]
Combining the formulas together the surface area of the triangular prism can be computed as:
[tex]\mathbf{S.A = ah+bh+ch+\dfrac{1}{2} \sqrt{ -a^4+2(ab)^2+2(ac)^2-b^4 +2(bc)^2-c^4}}[/tex]
[tex]\mathbf{S.A = (6\times9)+(6\times9)+(6\times9)+\dfrac{1}{2} \sqrt{ -6^4+2(6 \times 6)^2+2(6 \times 6)^2-6^4 +2(6 \times 6)^2-6^4}}[/tex]
S.A = 193.18 ft²
Learn more about the surface area of a triangular prism here:
https://brainly.com/question/26979119
