Answer:
To find the surface area, we must find the area of each and every individual side of this prism;
Before this we need to know the formula for area of a trapezoid:-
A = 1/2 x (b1 + b2) x h
where b1 is base one, and b2 is base two, h is the height
Now we find the area of the trapezoid above;
Bottom base 12, above base 6.
Height is 4.
Plug into our formula;
A = 1/2 x (b1 + b2) x h
A = 1/2 x (12 + 6) x 4
A = 1/2 x 18 x 4
A = 2 x 18
A = 36, the area of the trapezoid below will also be 36 because they are the same, so (36 + 36) = 72.
Now the area of the backside rectangle;
(formula for rectangle: A = L x W)
The width is 12.
The length is 3.
Plug in the values into our formula:-
A = L x W
A = 3 x 12
A = 36
Now the area of the front rectangle;
The base is 6.
The length is 3.
Plug in the values into our formula:-
A = L x W
A = 3 x 6
A = 18
Area of side rectangles(both have same area);
Base is 5.
Length is 3.
A = L x W
A = 3 x 5
A = 15, double of 15 (15 x 2) = 30.
Now we add all the areas:
72 + 36 + 18 + 30
= 156 inches, is the surface area.