Question

20.
A.find the total area
B. Find the volume

Please explain :)

Answer 1

check the first picture below, so the prism looks more or less like so.

now, check the second picture below, a triangular prism, is just 2 triangles and 3 rectangles.

so.. to get the total surface area of it, simply get the area of the rectangles and triangles, add them up, and that's the area of the prism.

the rectangles are just three each of 10x8
and to get the area of an equilateral triangle


`\bf \textit{area of an equilateral triangle}\\\\ A=\cfrac{s^2√(3)}{4}\qquad \begin{cases} s=\textit{length of a side}\\ ----------\\ s=8 \end{cases}\implies A=\cfrac{8^2√(3)}{4}\\\\ -------------------------------\\\\ \textit{thus the areas added} \\\\\\ (10\cdot 8)+(10\cdot 8)+(10\cdot 8)+\left((8^2√(3))/(4) \right)`

now, to get the volume of it, well, is just the area of a triangular face times the length, thus
`\bf volume=V= \cfrac{8^2√(3)}{4}\cdot 10`