Answer: 72 square centimeters
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Area of triangle ECD = (base)*(height)/2
Area of triangle ECD = 6*12/2
Area of triangle ECD = 72/2
Area of triangle ECD = 36 square cm
Subtract this area from the trapezoid area. This will get us the area of the parallelogram
Area of Parallelogram ABCE = (area of trapezoid ABDE) - (area of triangle ECD)
Area of Parallelogram ABCE = (180) - (36)
Area of Parallelogram ABCE = 144 square cm
The last step is to divide the area of the parallelogram in half. This is because the parallelogram is made of two congruent triangles (triangle ABE and triangle EBC). The two triangles ABE and EBC have equal areas
Area of triangle EBC = (1/2)*(area of parallelogram ABCE)
Area of triangle EBC = (1/2)*(144)
Area of triangle EBC = 72 square centimeters