In the given figure, D and E are two points on side BC of ΔABC such that BD = DE = EC. Prove that ar (ΔABD) = ar (ΔADE) = ar (ΔAEC).

Question

Philoid · Accepted Answer

Area of a triangle = 1/2 (Base × Height)

Now, draw AL perpendicular to BC and h be the height of ∆ABC i.e. AL

Thus, Height of ∆ABD = Height of ∆ADE = Height of ∆AEC

It is given that the bases BD, DE and EC of ∆ABD, ∆ADE and ∆AEC respectively are equal.

Now, since base and height both are equal of all the triangles therefore,

ar(∆ABD) = ar(∆ADE) = ar(∆AEC)