Q. 84.7( 20 Votes )

In the figure, AB

Answer :

i) Given AC || BF

Distance between two parallel lines is constant therefore if we consider AC as common base of ΔABC and ΔFAC then perpendicular distance between lines AC and BF will be same i.e height of triangles ΔABC and ΔFAC will be same

As ΔABC and ΔFAC are triangles with same base and equal height

area(ΔABC) = area(ΔFAC)

ii) since area(ΔABC) = area(ΔFAC)

add area(ACDE) to both sides

area(ΔABC) + area(ACDE) = area(ΔFAC) + area(ACDE) …(i)

From figure

area(ΔABC) + area(ACDE) = area(ABCDE) …(ii)

area(ΔFAC) + area(ACDE) = area(AFDE) …(iii)

using (ii) and (iii) in (i)

area(ABCDE) = area(AFDE)

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