D and E are two points on BC such that BD = DE = EC. Show that ar (ABD) = ar (ADE) = ar (AEC). Can you now answer the question that you have left in the ‘Introduction’ of this chapter, whether the field of Budhia has been actually divided into three parts of equal area?

Explanation

Area of triangle=`1/2 xx base xx height`
Since `BD=DE=CE`
`therefore` bases of all three triangles are equal.
Let BD=DE=CE be `x`
Construct altitude AP ,`therefore AP⊥BC`
Area of `/_\ABD=1/2 xx BD xx AP=1/2 xx x xx AP`
Area of `/_\ADE=1/2 xx DE xx AP=1/2 xx x xx AP`
Area of `/_\AEC=1/2 xx EC xx AP=1/2 xx x xx AP`
Since the areas of all 3 triangles is equal i.e `1/2 xx x xx AP`
Hence the field of Budhia has been actually divided into three parts of equal area