Given:
The dimensions of the triangle:
Base b = 4 in
Height h = 3 in
The dimensions of the rectangle:
Length l = 8 in
Height h = 5 in
Required:
Find the surface area of the triangular prism.
Explanation:
The surface area of the triangular prism is given by the formula:
[tex]A=2\times base\text{ area + perimeter of base }\times\text{ height}[/tex]
The base of the prism is a triangle.
The area of the triangle is given by the formula=
[tex]\frac{1}{2}\times base\times height[/tex]
So the area of the triangle =
[tex]\begin{gathered} =\frac{1}{2}\times4\times3 \\ =6\text{ in}^2 \end{gathered}[/tex]
The sides of the triangle are 3 in, 4 in., and 5 in.
The perimeter of the triangle P = 3 + 4+ 5 =12 in.
Thus the surface area of the triangular prism =
[tex]\begin{gathered} A=2\times6+12\times8 \\ A=12+96 \\ A=108\text{ in.}^2 \end{gathered}[/tex]
Final Answer:
The area of the given triangular prism is
[tex]108\text{ in.}^2[/tex]
