Question

the net below is used to form a triangular prism. find the surface area of the prism it forms. draw show your work here hint: to add the square root symbol (√□), type
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Explanation:

Step1: Calculate the area of the triangular faces

The formula for the area of a triangle is $A=\frac{1}{2}bh$. Here, $b = 7\ \text{yd}$ and $h=4\ \text{yd}$.
For one triangle: $A_1=\frac{1}{2}\times7\times4 = 14\ \text{yd}^2$.
Since there are 2 triangular faces: $A_{triangles}=2\times14=28\ \text{yd}^2$.

Step2: Calculate the area of the rectangular faces

There are 3 rectangular faces. Two have dimensions $7\times10$ and one has dimensions $7\times10$ (because the prism has two congruent rectangles with sides $7$ and $10$ and one rectangle with sides $7$ and $10$).
The formula for the area of a rectangle is $A = lw$.
For each $7\times10$ rectangle: $A_{rect}=7\times10 = 70\ \text{yd}^2$.
Since there are 3 such rectangles: $A_{rectangles}=3\times70=210\ \text{yd}^2$.

Step3: Calculate the total surface area

The total surface area $A = A_{triangles}+A_{rectangles}$.
$A=28 + 210=238\ \text{yd}^2$.

Answer:

$238\ \text{yd}^2$