The prism in the picture has 6 sides, three are shown.
We will have to calculate the area of each of them and sum.
The front and back surfaces are the same and are a trapezoid with height 12 cm, base 27cm and top 6cm.
We can use the area formula for trapezoid:
[tex]A=\frac{\mleft(a+b\mright)}{2}h[/tex]Where, "a" and "b" are the base and top, and "h" is the height.
So:
[tex]A_{1,2}=\frac{6+27}{2}12=33\cdot6=198[/tex]So we have the area of the front surface 198 cm², since the back is the same we have two surfaces.
The top surface is a rectangle with dimensions 30 cm and 6cm, so its area is:
[tex]A_3=30\cdot6=180[/tex]It is 180 cm².
The surface at the right is also a rectangle with measures 30cm and 20cm, so:
[tex]A_4=30\cdot20=600[/tex]600 cm².
The surface of the left not appearing in the picure is also a rectangle and have measures 13cm and 30cm, so the area is:
[tex]A_5=30\cdot13=390[/tex]390 cm².
And the last is the bottom one, which is also a rectangle, with measures 27cm and 30cm.
[tex]A_6=30\cdot27=810[/tex]810 cm².
Now that we have all the areas,
