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, $b = 9\ \text{m}$ and $h = 7\ \text{m}$.
For one triangle: $A_1=\frac{1}{2}\times9\times7=\frac{63}{2}= 31.5\ \text{m}^2$.
Since there are 2 triangular faces: $A_{triangles}=2\times31.5 = 63\ \text{m}^2$.

Step2: Calculate the area of the rectangular faces

There are 3 rectangular faces.

• One with dimensions $9\times15$: $A_{9 - 15}=9\times15 = 135\ \text{m}^2$.
• Two with dimensions $14\times15$: $A_{14 - 15}=2\times14\times15=420\ \text{m}^2$.

Step3: Calculate the total surface area

The total surface area $A = A_{triangles}+A_{9 - 15}+A_{14 - 15}$.
$A=63 + 135+420=531\ \text{m}^2$.

Answer:

$531\ \text{m}^2$