The figure shows an equilateral ΔABC of side 10 cm and a right angle ΔBDC whose side BD = 8 cm and ∠D=90∘.
The area of the shaded portion is
19.3
In ΔBDC,
DC2=102−82
DC2=62
(6-8-10 Pythagoras Triplet)
Area of shaded region = Area ΔABC− Area ΔBDC
=√34(10)2−(12×6×8)
=(1.732)(100)4−24
=43.3−24
=19.3 cm2