ANSWER :
The height of the prism is h = 7 ft
The are of the base is B = 12 ft^2
The perimeter of the base is P = 18 ft
Fill in the formula. S = 2x12 + 18x7
The surface area of the triangular prism is 150 ft^2
EXPLANATION :
The given formula for the surface area is :
[tex]S=2B+Ph[/tex]where B = Base area
P = perimeter of the bases
h = height of the prism
The height of the prism is h = 7 ft
The base is a triangle with dimensions of b = 8 ft and a height h = 3 ft
The area of a triangle is :
[tex]\begin{gathered} A=\frac{1}{2}bh \\ \\ A=\frac{1}{2}(8)(3) \\ \\ A=12ft^2 \end{gathered}[/tex]The are of the base is B = 12 ft^2
The perimeter of the base is 5 + 5 + 8 = 18 ft, so P = 18 ft
Substitute the results in the formula :
[tex]\begin{gathered} S=2B+Ph \\ S=2(12)+18(7) \\ S=150ft^2 \end{gathered}[/tex]