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What is the lateral surface area of this triangular prism?

What is the lateral surface area of this triangular prism?-example-1
User Kumaresh Babu N S
by
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1 Answer

11 votes
11 votes

first off let's take a peek at what the slanted side of the base is hmmm


\textit{using the pythagorean theorem} \\\\ c^2=a^2+b^2 \qquad \begin{cases} c=hypotenuse\\ a=\stackrel{adjacent}{3}\\ b=\stackrel{opposite}{3}\\ \end{cases}\implies c^2=3^2+3^2 \\\\\\ c^2=3^2(1+1)\implies c^2=3^2(2)\implies c=√(3^2(2))\implies c=3√(2)

Check the picture below, the lateral surface, namely just the sides, excluding top and bottom, is really just 3 rectangles, so let's get their area and sum them up.


\stackrel{\textit{\large Areas}}{\stackrel{two~rectangles}{2(3\cdot 6)}~~ +~~\stackrel{rectangle}{(6\cdot 3√(2))}}\implies 36+18√(2)~~ \approx ~~61.46

What is the lateral surface area of this triangular prism?-example-1
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