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)

Rate this question :

In the figure, diAP- Mathematics

ABCD is a paralleAP- Mathematics

In the figure, XYAP- Mathematics

In a triangle ABCAP- Mathematics

In the figure, ∆AAP- Mathematics

P and Q are any tAP- Mathematics

Show that the diaAP- Mathematics

In the figure, ∆AAP- Mathematics

A farmer has a fiAP- Mathematics

In the figure, ifAP- Mathematics