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Figures on the Same Base and Between the Same Parallels

Question 11 i...

Question

Question 11 (ii)
In the given figure, ABCDE is a pentagon. A line through B parallel to AC meets DC produced at F. Show that:

(ii) ar(AEDF) = ar(ABCDE)

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Solution

It can be observed that,
$A r e a (Δ A C B) = A r e a (Δ A C F)$
Then, $A r e a (Δ A C B) + A r e a (A C D E) = A r e a (A C F) + A r e a (A C D E)$
[Adding Area(ACDE) on both sides]
$\Rightarrow$ Area(ABCDE) = Area(AEDF)

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Figures on the Same Base and Between the Same Parallels

Standard IX Mathematics

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