ABCDE is a pentagon.A line passing through B parallel to AC meets DC produced at F.Show that

ar(ACB)=ar(ACF)

ar(AEDF)=ar(ABCDE)

explain with figure

Given : ABCDE is a Pentagon. 

Construction : join AF anf BC

Proof :

(1)

Since and are on the same base AC and between the same parallels AC and BF. So,

Hence Proved.

(2)

Hence Proved.

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(i) ΔACB and ΔACF lie on the same base AC and are between

The same parallels AC and BF.

∴ Area (ΔACB) = Area (ΔACF)

(ii) It can be observed that

Area (ΔACB) = Area (ΔACF)

⇒ Area (ΔACB) + Area (ACDE) = Area (ACF) + Area (ACDE)

⇒ Area (ABCDE) = Area (AEDF)

Hope it helps!
THUMBS UP PLEASE!

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