Answer:
Option C. [tex]543\ in^{2}[/tex]
Step-by-step explanation:
we know that
The surface area of the triangular prism (foam block) is equal to
[tex]SA=2B+PH[/tex]
where
B is the area of the triangular base
P is the perimeter of the triangular base
H is the height of the triangular prism (distance between the triangular faces)
Find the area of the base B
[tex]B=\frac{1}{2}bh[/tex]
substitute values
[tex]B=\frac{1}{2}(12)(6)=36\ in^{2}[/tex]
Find the perimeter of the base
[tex]P=(13.4+12+6)=31.4\ in[/tex]
Find the surface area
[tex]SA=2B+PH[/tex]
[tex]SA=2(36)+(31.4)(15)=543\ in^{2}[/tex]
