First find the area of the triangle.
[tex]\sf A=\dfrac{1}{2}bh[/tex]
[tex]\sf A=\dfrac{1}{2}(6)(12)[/tex]
[tex]\sf A=36cm^2[/tex]
ABCE is a parallelogram, this means that the area of triangle ABE is equal to the area of triangle EBC. The are of the entire trapezoid is 180 square centimeters, we already found the area of the triangle, so that leaves us with:
[tex]\sf 180-36=144[/tex]
So the area of the entire parallelogram must be 144 square centimeters. So each half of the parallelogram must be equal to:
[tex]\sf 144\div 2=\boxed{\sf 72cm^2}[/tex]
