Question

ABCD is a parallelogram. P is any point on the side AB. If the area of a parallelogram is 16cm square find the area of triangle PDC?​

Answer 1

Answer:

Step-by-step explanation:

Given,

ABCD is a ||gm and P is a pt on CD

R.T.P : Area of triangle APD+Area of triangle BCP = Area of triangle ABP

Now,

triangle APD + triangle BCP +triangle ABP = ||gm ABCD   ...(i)

but,

by the theorem on area,13.4,

which states that the area of a triangle lying on the same base and between the same parallel lines as of the ||gm has area equal to half of that of the parallelogram.

=>area of triangle ABP=1/2 area of ||gm ABCD   ...(ii)

from (i) and (ii),we have,

area of trian. APD +area of trian.BCP + 1/2 area of ||gm ABCD=area of ||gm ABCD

area of trian. APD + area of trian. BCP=(1-1/2)area of ||gm ABCD

                                                            =1/2 area of ||gm ABCD

                                                            =Area of triangle APB  (from (ii)).

Hence, proved.

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