Answer :

Given: AB = BC = AC = a (let) = 10 cm


BD = 8 cm


Now,


Area of an equilateral triangle (∆ABC) =


=


= 25√3 cm2


= 43.3 cm2


Now, in ∆DBC


Base2 + Perpendicular2 = Hypotenuse2


DC2 + DB2 = BC2


DC2 = BC2-BD2


DC2 = 102-82


DC2 = 100-64


DC2 = 36 cm2


DC = 6 cm


Now,


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


= 1/2 × DC × BC


= 1/2 × 6 cm × 8 cm


= 1/2 × 48 cm2


= 24 cm2


Now,


Area of shaded region = ∆ABC - ∆DBC


= 43.3 cm2 – 24 cm2


= 19.3 cm2


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