Question

Look at the parallelogram ABCD shown below.



Using complete sentences, explain how the formula for the area of parallelogram ABCD is derived.

Answer 1

Assumption: We already know the formula for the area of a triangle.
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By the Area Addition Postulate, the area of Parallelogram ABCD is equal to the sum of the areas of triangular regions ADC and ABC.

Area of Parallelogram ABCD = Area of Triangle ADC + Area Triangle ABC
Area of Parallelogram ABCD = (1/2)(b)(h) + (1/2)bh
Area of Parallelogram ABCD = (1/2) h (b + b)
Area of Parallelogram ABCD = (1/2) h (2b)
Area of Parallelogram ABCD = hb = bh

Answer 2

thanks