Question

prove ar (ABCDE) = ar (TRIANGLE APQ)​

Answer 1

Answer:

Here,

In Quad ADQE,

triangle ADE& AQD have same base AD and live between same parallels AD&QE.

So,ar triangle ADE=ar triangle AQD

Again,

In Quad ACPB,

triangle PAC&ABC lie on same base AC and between same parallels BP&AC.

So,arPAC = ar ABC.

Now,

ar (ABCDE)=ar ABC +ar ACD+ar AED.----(1)

and,ar APQ=arAPC+ar ACD +ar ADQ.

OR ,ar APQ=ar ABC+ar ACD+ar AED-----(2).

AS,(1)=(2).

THEREFORE,ar(ABCDE)=ar(APQ).