Question

To find the surface area of a triangular prism, use the formulaS= 2B + Ph where B is the area of the base, P is the perimeter of thebases, and h is the height of the prism.The height of the prism is_____ftThe area of the base is_____ftThe perimeter of the base is_____ftFill in the formula. S= 2.____+____X_____The surface area of the triangular prism is_____ft

Answer 1

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 :

`S=2B+Ph`

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 :

`\begin{gathered} A=(1)/(2)bh \\ \\ A=(1)/(2)(8)(3) \\ \\ A=12ft^2 \end{gathered}`

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 :

`\begin{gathered} S=2B+Ph \\ S=2(12)+18(7) \\ S=150ft^2 \end{gathered}`