Q11 of 77 Page 15

If P is any point in the interior of a parallelogram ABCD, then prove that area of the triangle APB is less than half the area of parallelogram.

Construction: Draw DN⊥ AB and PM⊥ AB.

Proof: Area of parallelogram ABCD = AB * DN


Area (Δ APB) = (AB * PM)


= AB * PM < AB * DN


= (AB * PM) < (AB * DN)


= Area (Δ APB) < Area of parallelogram ABCD



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