Question

Area of the shaded segment=
https://media.glynlyon.com/g_geo_2012/8/group103bb.gif

Answer 1

The area of the equilateral triangle is
\[
\frac{a^2 \sqrt 3 }4= \frac{6^2 \sqrt 3 }4= 9\sqrt 3
\]

Answer 2

The area of the sector is
\[
\frac{36 \pi}6= 6 \pi
\]

Answer 3

Shaded area is
\[
6 \pi - 9\sqrt 3\approx 3.2611
\]