Answer:
Part 1) The surface area of the triangular prism is [tex]SA=660\ cm^{2}[/tex]
Part 2) The surface area of the trapezoidal prism is [tex]SA=2,864\ cm^{2}[/tex]
Step-by-step explanation:
Part 1) Find the surface area of the triangular prism
we know that
The surface area is equal to
[tex]SA=2B+PL[/tex]
where
B is the area of the triangular base of the prism
P is the perimeter of the base of the prism
L is the length of the prism
Find the area of the triangular base B
[tex]B=\frac{1}{2}(10)(12)=60\ cm^{2}[/tex]
Find the perimeter of the base P
[tex]P=10+13+13=36\ cm[/tex]
[tex]L=15\ cm[/tex]
substitute the values
[tex]SA=2(60)+(36)(15)=660\ cm^{2}[/tex]
Part 2) Find the surface area of the trapezoidal prism
we know that
The surface area is equal to
[tex]SA=2B+PL[/tex]
where
B is the area of the trapezoid base of the prism
P is the perimeter of the base of the prism
L is the length of the prism
Find the area of the trapezoid base B
[tex]B=\frac{1}{2}(28+15)(8)=172\ cm^{2}[/tex]
Find the perimeter of the base P
[tex]P=15+28+10+10=63\ cm[/tex]
[tex]L=40\ cm[/tex]
substitute the values
[tex]SA=2(172)+(63)(40)=2,864\ cm^{2}[/tex]
