Question

A right triangular prism is shown. Find (A) the total surface area and (B) the volume. You must show formulas and your work.

Answer 1

Hello!

We are going to use the rectangular prism of the image as a guide:

First of all, the AC segment is calculated using the Pythagoras' theorem:

$AC= \sqrt{ AB^{2}+ BC^{2} } =\sqrt{ 10^{2}+ 8^{2} }=12,81 m$

(A) The surface area of a prism is the sum of the surface areas of each face. 

For the 2 triangles  ABC and DEF

$A=2*(1/2*b*h)=2*(1/2*8m*10m)=80m$

For the ABEF Rectangle

$A=w*l=10,77m*10m=107,7m^{2}$

For the ACDE Rectangle

$A=w*l=10,77m*12,81m=137,96 m^{2}$

For the BCDF Rectangle 

$A=w*l=10,77m*8m=86,16 m^{2}$

To finish you need to sum up the areas of each face:

$SA=2A_{ABC}+ A_{ABEF}+A_{ACDE}+A_{BCDF}= \\ 80 m^{2} +107,7m^{2} +137,96m^{2} +86,16m^{2} =411,82m^{2}$

(B) The volume of a prism is the product of the area of its base and the height of the prism. In this case, the base is a triangle so the formula and the calculations for the volume are as follows

$V= \frac{1}{2} *w*h*l= \frac{1}{2}* 8m*10m*10,77m=430,8m^{3}$