To solve this we are going to use the formula for the total surface area of a trapezoidal prism:Â
where
is the total surface area of the trapezoidal prism
is the lateral surface area of the trapezoidal prismÂ
is the Area of base (area of the trapezoid)
To findÂ
, we are going to use the formula for the lateral surface area of a trapezoid:Â
whereÂ
is the larger base of the trapezoidÂ
is the shorter base of the trapezoidÂ
andÂ
are the other sides of the trapezoid
Remember that the parallel sides of a trapezoid are its bases, so:
andÂ
. We also know that the other sides are each 4m, so:Â
andÂ
. Also, since the prism is 2m tall,Â
.  Lets replace those values in our formula to findÂ
:
Now, to find the area of the base, we are going to use the formula for the area of a trapezoid:Â
where
is the area of the trapezoid
is the altitude of the trapezoidÂ
is the larger base of the trapezoidÂ
is the shorter base of the trapezoidÂ
We know for our problem thatÂ
,Â
, andÂ
. Lets replace those values in our formula to findÂ
:
Now that we haveÂ
andÂ
, we can finally use the formula for the total surface area of a trapezoidal prism:
We can conclude that the surface area of the prism is 71 square meters.