In the given figure, PQRS and ABRS are parallelograms and X is any point on side BR. Show that .
$a r (Δ A X S) = \frac{1}{2} a r (P Q R S)$ [4 MARKS]

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Solution

Concept : 1 Mark
Application : 1 Mark
Proof : 2 Marks

Consider parallelogram PQRS and parallelogram ABRS.
As these lie on the same base SR and are between the same parallel lines PB and SR,
ar(PQRS) = ar(ABRS) .....(1)

Consider $Δ A X S$ and parallelogram ABRS.
As these lie on the same base AS and are between the same parallel lines AS and BR,
$∴ a r (Δ A X S) = \frac{1}{2} a r (A B R S) . . . (2)$

From equations(1) and(2), we obtain
$a r (Δ A X S) = \frac{1}{2} a r (P Q R S)$

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In the given figure, PQRS and ABRS are parallelograms and X is any point on side BR. Show that

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