I think u may have figure in the book.

1) To prove :ar(ΔBDE) =1/4 ar(ΔABC)

proof : we have given ABC is a equilateral triagle

so AB= BC = CA

we have also given that D is the mid point of BC

and BDE is a also an equilateral triangle

so BD = DE = EB

if u remember than we have studied heron't formula in which we have read that area of equilateral triangle = √3a²/4 where a is the side

so let the side of ΔABC = a

area = √3a²/4

and the side of ΔBDE = a/2 because D is the median of side of BC so BC = a of 1/2 BC =a/2

and ar (ΔBDE) = √3/4 × (a/2)²

= √3a²/4 ×1/4

= 1/4ar(ΔABC) ( ∵√3a²/4 = ar(ΔABC)