Answer:
The surface area is
Step-by-step explanation:
we know that
The tent is a triangular prism
see the attached figure to better understand the problem
The surface area of the triangular prism is equal to
where
B is the area of the triangular face
P is the perimeter of the triangular face
L is the length of the prism
<em>Find the area of the triangular face B</em>
<em>Find the perimeter of the triangular face P</em>
we have
substitute the values
So before I put the equation into standard form, I'm first going to be putting it into vertex form. Since the vertex appears to be (-1,7), plug that into the vertex form formula:
Next, we need to solve for a. Looking at this graph, another point that is in this line is the y-intercept (0,5). Plug (0,5) into the x and y placeholders and solve for a as such:
Now we know that <u>our vertex form equation is y = -2(x + 1)^2 + 7.</u>
However, we need to convert this into standard form still, and we can do it as such:
Firstly, solve the exponent:
Next, foil -2(x^2+2x+1):
Next, combine like terms and <u>your final answer will be: </u>