Aright triangular prism is shown. find (a) the total surface area and (b) the volume. you must show formulas and your work. 10m height 8m width 10.77m

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:



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

For the 2 triangles  ABC and DEF



For the ABEF Rectangle



For the ACDE Rectangle



For the BCDF Rectangle 



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



(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