Question

Find the surface area

Answer 1

Check the picture below.

so hmmm let's find the length of the slanted side, namely the hypotenuse of the triangle with sides of 9 and 7(half of 14).

`\begin{array}{llll} \textit{using the pythagorean theorem} \\\\ c^2=a^2+o^2\implies c=√(a^2 + o^2) \end{array} \qquad \begin{cases} c=hypotenuse\\ a=\stackrel{adjacent}{9}\\ o=\stackrel{opposite}{7} \end{cases} \\\\\\ c=√( 9^2 + 7^2)\implies c=√( 81 + 49 ) \implies c=√( 130 )`

so now let's get the areas of those triangles and those rectangles.

`\stackrel{\textit{two triangles}}{2\left[\cfrac{1}{2}(14)(9) \right]}~~ + ~~\stackrel{\textit{left and right rectangles}}{2(√(130))(20)}~~ + ~~\stackrel{\textit{bottom rectangle}}{(20)(14)} \\\\\\ 126+40√(130)+280\implies 406+40√(130) ~~ \approx ~~ \text{\LARGE 862.07}~cm^2`