Question

What is the surface area and volume? PLEASE EXPLAIN IN DETAIL.

Answer 1

Check the picture below.

so to find the surface area of the triangular prism, we simply add the areas of each of the figures composing it, as you can see is really just 2 triangles an 3 rectangles.

`\bf \stackrel{\textit{\Large Areas}}{\stackrel{triangles}{2\left[ \cfrac{1}{2}(4)(3) \right]}+\stackrel{\textit{rectangles}}{(3\cdot 10)+(4\cdot 10)+(5\cdot 10)}}\implies 12+30+40+50\implies 132`

now, to get the volume is simply the area of the triangular face times the length, well, we know the area of one of the triangles is 6, times 10 is just 6*10 = 60.