The surface area of the given prism is the sum of areas of all sides.
From the given figure, we have :
2 Triangles with a base of 9 ft and a height of 7.6 ft
1 rectangle with a length of 13 ft and a width of 10 ft
1 rectangle with a length of 13 ft and a width of 8 ft
1 rectangle with a length of 13 ft and a width of 9 ft
The formula for the area of a triangle is :
[tex]A=\frac{1}{2}\times Base\times Height[/tex][tex]A=\frac{1}{2}\times9\times7.6[/tex][tex]A=34.2[/tex]Since there are two triangles, the total area of the triangle is :
[tex]A=2\times34.2=68.4[/tex]The formula for the area of the rectangle is :
We can add the three triangles together.
[tex]A=(13\times10)+(13\times8)+(13\times9)[/tex][tex]A=130+104+117[/tex][tex]A=351[/tex]Now we have the areas of the sides, take the sum of these areas to find the surface area.
[tex]\text{Surface Area = 68.4 + 351}[/tex][tex]\text{Surface Area = 419.4 ft\textasciicircum{}2}[/tex]