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Areas of Parallelograms and Triangles
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15/07/2021 1:01 pm
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In Figure, PQRS and ABRS are parallelograms and X is any point on side BR. Show that
(i) ar (PQRS) = ar (ABRS)
(ii) ar (AXS) = ar \(\frac{1}{2}\) (PQRS)
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15/07/2021 1:02 pm
(i) Parallelogram PQRS and ABRS lie on the same base SR and in-between the same parallel lines SR and PB.
∴ ar(PQRS) = ar(ABRS) — (i)
(ii) ΔAXS and parallelogram ABRS are lying on the same base AS and in-between the same parallel lines AS and BR.
∴ ar(ΔAXS) = \(\frac{1}{2}\) ar(ABRS) — (ii)
From (i) and (ii), we find that,
ar(ΔAXS) = \(\frac{1}{2}\) ar(PQRS)