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:
[tex]AC= \sqrt{ AB^{2}+ BC^{2} } =\sqrt{ 10^{2}+ 8^{2} }=12,81 m[/tex]
(A) The surface area of a prism is the sum of the surface areas of each face.
For the 2 triangles ABC and DEF
[tex]A=2*(1/2*b*h)=2*(1/2*8m*10m)=80m[/tex]
For the ABEF Rectangle
[tex]A=w*l=10,77m*10m=107,7m^{2}[/tex]
For the ACDE Rectangle
[tex]A=w*l=10,77m*12,81m=137,96 m^{2}[/tex]
For the BCDF Rectangle
[tex]A=w*l=10,77m*8m=86,16 m^{2}[/tex]
To finish you need to sum up the areas of each face:
[tex]SA=2A_{ABC}+ A_{ABEF}+A_{ACDE}+A_{BCDF}= \\ 80 m^{2} +107,7m^{2} +137,96m^{2} +86,16m^{2} =411,82m^{2} [/tex]
(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
[tex]V= \frac{1}{2} *w*h*l= \frac{1}{2}* 8m*10m*10,77m=430,8m^{3} [/tex]
