Answer:
[tex]TSA=384\ in^2[/tex]
Step-by-step explanation:
The formula for calculate the Total surface area of a triangular prism is:
[tex]TSA=LSA+2B[/tex]
Where "LSA" is the the lateral surface area of the prism and "B" is the area of the base.
The formula for calculate the Lateral surface area of a triangular prism is:
[tex]LSA=PH[/tex]
Wherre "P" is the perimeter of the base and "H" is the height of the prism.
Lateral surface area
Since the perimeter of the base is the sum of its sides, this is:
[tex]P=20\ in+\12\ in+16\ in\\\\P=48\ in[/tex]
You can identify in the figure that:
[tex]H=4\ in[/tex]
Then, susbstituting values, you get:
[tex]LSA=(48\ in)(4\ in)\\\\LSA=192\ in^2[/tex]
Total surface area
The base is a triangle, then its area can be found with this formula:
[tex]B=\frac{bh}{2}[/tex]
Where "b" is the base of the triangle and "h" is the height.
In this case, this is:
[tex]B=\frac{12\ in*16\ in}{2}=96\ in^2[/tex]
Therefore, substituting the known values into the formula, you get that the total surface area is:
[tex]TSA=192\ in^2+2(96\ in^2)\\\\TSA=384\ in^2[/tex]
