If ABCD is a parallelogram, then prove that ar(Δ ABD) = ar(Δ BCD) = ar(Δ ABC)=ar(Δ ACD) = ar(|| gm ABCD)

Question

If ABCD is a parallelogram, then prove that ar(&#x394; ABD) = ar(&#x394; BCD) = ar(&#x394; ABC)=ar(&#x394; ACD) = ar(|| gm ABCD)

Philoid · Accepted Answer

We know that,

Diagonal of parallelogram divides it into two quadrilaterals.

Since,

AC is the diagonal

Then, Area (ΔABC) = Area (ΔACD)

= Area of parallelogram ABCD (i)

Since,

BD is the diagonal

Then, Area (ΔABD) = Area (ΔBCD)

= Area of parallelogram ABCD (ii)

Compare (i) and (ii), we get

Therefore,

Area (ΔABC) = Area (ΔACD) = Area (ΔABD) = Area (ΔBCD) = Area of parallelogram ABCD