Mathematics
In the figure (2) given below, PQRS and ABRS are parallelograms, and X is any point on the side BR. Show that
area of ∆AXS = area of || gm PQRS.
Theorems on Area
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Answer
From figure,
Since, PB is a straight line and PQ || SR so,
PB || SR.
|| gm PQRS and ABRS are on the same base SR and between the same parallel lines PB and SR.
So, Area of ||gm PQRS = Area of ||gm ABRS ………(i)
∆AXS and || gm ABRS are on the same base AS and between the same parallel lines AS and BR.
So, Area of ∆AXS = Area of ||gm ABRS
= area of ||gm PQRS [From (i)]
Hence, proved that Area of ∆AXS = Area of || gm PQRS.
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