Question

I challenges brainly expert to solve my question

Answer 1

see the attachment,
AT shows the altitude of ΔABC
Let ∠ABC = β
then, sinβ = AT/AB
AT = AB sinβ
means altitude of ΔABC = AB sinβ
now, area of ΔABC = 1/2 base * height
                                 = 1/2 BC*AB sinβ = 24 -------(1)
a/c to question,
   AM = MB = 1/2 AB-----------------------(2)
now, use cosβ for ΔBDM,
 cosβ = BD/MB
BD = MB cosβ = 1/2AB cosβ [from eqn (2)
BD =1/2 AB cosβ ---------------------------(3)

again, use tanβ for ΔBEC,
 tanβ = CE/BC
CE = BC tanβ---------------------------------(4)

now, area   of ΔBDE = 1/2 base *height
                         = 1/2 BD *CE
     use eqns (3) and (4)
  area of ΔBDE = 1/2 (1/2AB cosβ) (BC tanβ)
                         = 1/4 AB*BC cosβ×sinβ/cosβ = 1/4AB*BC sinβ
now from equation (1)
area of ΔBDE = 1/2(area of ΔABC) = 24/2 = 12