# Q: 5     In Fig. 9.17, PQRS and ABRS are parallelograms and X is any point on side BR. Show that            (i)   $\small ar(PQRS)=ar(ABRS)$            (ii)  $\small ar(AXS)=\frac{1}{2}ar(PQRS)$

M manish

(i) Parallelogram PQRS and ABRS are on the same base RS and between the same parallels RS and PB.
Therefore,  $\small ar(PQRS)=ar(ABRS)$............(i)
Hence proved

(ii) $\Delta$AXS and ||gm ABRS are on the same base AS and between same parallels AS and RB.
Therefore, ar ($\Delta$AXS) = 1/2 . ar(||gm ABRS)............(ii)

Now, from equation (i) and equation (ii), we get

$\small ar(AXS)=\frac{1}{2}ar(PQRS)$

Hence proved.

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