# In the given figu

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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