Check the picture below.

so, to get the area of the triangles, we can simply run a perpendicular line from the top to the base, and end up with a right-triangle with a base of 22 and a hypotenuse of 34, let's find the altitude.

$\bf \textit{using the pythagorean theorem}
\\\\
c^2=a^2+b^2\implies \sqrt{c^2-a^2}=b
\qquad 
\begin{cases}
c=hypotenuse\\
a=adjacent\\
b=opposite\\
\end{cases}
\\\\\\
\sqrt{34^2-22^2}=b\implies \sqrt{672}=b$

so then the surface area of the triangular prism is,

$\bf \stackrel{\textit{left and right}}{2(34\cdot 76)}~~+~~\stackrel{\textit{bottom}}{(44\cdot 76)}~~+~~\stackrel{\textit{front and back}}{2\left[\cfrac{1}{2}(44)(\sqrt{672}) \right]}
\\\\\\
8512~~+~~(44)(\sqrt{672})\qquad \approx\qquad 9652.61036291978$

5 0

3 years ago

PLS HELP find the unknown side of the triangle below (round to the nearest tenth)

Nonamiya [84]

22.9 is the closest but not exact. It was probably rounded off.

I used the formula: leg^2+leg^2=hypotenuse^2

(You can use that formula for any right triangle.)

7 0

4 years ago