Question

PQRS and ABRS are parallelogram and x is any point on the side BR. show that
(I) ar(PQRS) = ar(ABRS)
(ii) ar$\left(\Delta AXS\right)=\frac{1}{2}ar\left(PQRS\right)$

Answer 1

R.E.F.Image.

As $AB\parallel PQ\parallel RS$

$\Rightarrow$ any perpendicular from

PQ to RS would have same

length as that given AB to RS

As $ar\left(PQRS\right)=base\times height=RS\times height$

& $ar\left(ABRS\right)=base\times height=RS\times height$

$\Rightarrow ar\left(PQRS\right)=ar\left(ABRS\right)$

NOW, $ar\left(AXS\right)=\frac{1}{2}\times Base\times height=\frac{1}{2}\times AS\times MX$

& $ar\left(ABRS\right)=ar\left(PQRS\right)=base\times height=\left(MX\right)\times \left(AS\right)$

$\Rightarrow ar\left(AXS\right)=\frac{1}{2}ar\left(PQRS\right)$