Answer:
The surface area of the triangular prism is [tex]1,152\ yd^{2}[/tex]
Step-by-step explanation:
we know that
The surface area of the triangular prism 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
step 1
Find the area of the base B
[tex]B=\frac{1}{2}bh[/tex]
we have
[tex]b=51\ yd[/tex]
[tex]h=12\ yd[/tex]
substitute
[tex]B=\frac{1}{2}(51)(12)=306\ yd^{2}[/tex]
step 2
Find the perimeter of the base P
[tex]P=37+20+51=108\ yd[/tex]
step 3
Find the surface area
[tex]SA=2B+PH[/tex]
we have
[tex]B=306\ yd^{2}[/tex]
[tex]P=108\ yd[/tex]
[tex]H=5\ yd[/tex]
substitute
[tex]SA=2(306)+108(5)=1,152\ yd^{2}[/tex]
