# 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. - Mathematics

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.

#### Solution

Draw DN ⊥ AB and PM ⊥ AB.
Now,

Area  (ΙΙ^(gm) ABCD) = AB xx DN , ar (ΔAPB ) = 1/2 (AB xx PM)

Now , PM < DN

⇒  AB xx PM < AB xx DN

⇒   1/2 (AB xx PM) < 1/2 (AB xx DN)

⇒  Area ( ΔAPB ) <1/2 ar ( Parragram ABCD)

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#### APPEARS IN

RD Sharma Mathematics for Class 9
Chapter 14 Areas of Parallelograms and Triangles
Exercise 14.3 | Q 17 | Page 46