Question

abcde IS A PENTAGON . BP drawn parallel to AC meets DC produced at P and EQ drawn parallel to AD meet CD produced at Q . prove that ar(ABCDE)=ar(APQ).

Answer 1

i have solved in the above image. hope i helped

Answer 2

Take triangles ABC and APC.

Both of them lie on the same base AC and in between same parallel lines AC and BP.

So, ar(ABC) = ar(APC)   [Triangles which lie on the same base and in between same parallel lines are always equal in area]             - 1

Take triangles AED and AQD.

Both of them lie on the same base AD and in between same parallel lines AD and EQ.

So, ar(AED) = ar(AQD)          -2

Adding 1 and 2,

ar(ABC) + ar(AED) = ar(APC) + ar(AQD)

Now, add ACD on both sides,

ar(ABC) + ar(AED) + ar(ACD) = ar(APC) + ar(AQD) + ar(ACD)

ar(ABCDE) = ar(APQ)

Hence proved.