Question

The image is listed below. Any help would be appreciated!

Answer 1

Check the picture below.

part A

since the base of the triangular base is 16, and the altitude "h" splits the base in two equal halves, half that is just 8, so we're looking at a right triangle with a hypotenuse of 17 and a side of 8, thus

`\textit{using the pythagorean theorem} \\\\ c^2=a^2+b^2\implies √(c^2 - a^2)=b \qquad \begin{cases} c=\stackrel{hypotenuse}{17}\\ a=\stackrel{adjacent}{8}\\ b=\stackrel{opposite}{h}\\ \end{cases} \\\\\\ √(17^2-8^2)=h\implies √(225)=h\implies \boxed{15=h}`

part B

well, the prism is simply two triangles and 3 rectangles, le's simply add their areas.

`\stackrel{two~triangles}{2\left[ \cfrac{1}{2}(\stackrel{base}{16})(\stackrel{height}{15}) \right]}~~ + ~~\stackrel{two~rectangles}{2(20)(17)}~~ + ~~\stackrel{one~rectangle}{(20)(16)} \\\\\\ 240~~ + ~~680~~ + ~~320\implies \text{\LARGE 1240}`