Answer:
[tex]LA=755\ m^{2}[/tex], [tex]SA=785\ m^{2}[/tex]
Step-by-step explanation:
Part 1) Find the lateral area of the given prism
we know that
The lateral area of the prism is equal to
[tex]LA=PL[/tex]
where
P is the perimeter of the triangular base
L is the length of the prism
Find the perimeter P
[tex]P=5+6+11.21=22.21\ m[/tex]
we have
[tex]L=34\ m[/tex]
substitute
[tex]LA=(22.21)(34)=755\ m^{2}[/tex]
Part 2) Find the surface area of the given prism
we know that
The surface area of the prism is equal to
[tex]SA=2B+LA[/tex]
where
B is the area of the triangular base
LA is the lateral area of the prism
Find the area B
[tex]B=(1/2)(5)(6)=15\ m^{2}[/tex]
we have
[tex]LA=755\ m^{2}[/tex]
substitute
[tex]SA=(2)(15)+755=785\ m^{2}[/tex]
