Surface Area of Prisms
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Find the surface area of the following triangular prism, correct to the nearest \(\rm{m}^2\).
This triangular prism has 5 faces - Two identical triangles (front and back) and three different rectangles. The triangle is right-angled, whose two sides are 5m and 3m. So the third side (hypotenuse) is:
\[= \sqrt{5^2+3^2}= \sqrt{34}~\text{m}\]$$
\begin{aligned}
\text{Total Surface Area}&=\text{Area of two triangles + Area of 3 rectangles}\\
&=2\times \frac{1}{2}\times 3\times 5+12\times 5+3\times 12 + 12\times \sqrt{34}\\
&=15+60+36+12\times 5.83095\\
&=123+69.97\\
&=181~\text{m}^2
\end{aligned}
$$
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