In the given figure, ABCDEF is a regular hexagon whose side is 6 cm. APF, QAB, DCR and DES are equilateral triangles. What is the area (in cm²) of the shaded region?

Solution (By Examveda Team)

Area of Hexagon $$ = 6 \times \frac{{\sqrt 3 }}{4}{\left( 6 \right)^2} = 54\sqrt 3 {\text{ c}}{{\text{m}}^2}$$
Area of one part of Hexagon $$ = \frac{{54}}{6}\sqrt 3 = 9\sqrt 3 $$
Required area $$ = 54\sqrt 3 + 2 \times 9\sqrt 3 = 72\sqrt 3 {\text{ c}}{{\text{m}}^2}$$

Alternate Solution:
Counting the equilateral triangle figure = 8
Area of equilateral triangle is equal to $$ = 8 \times \frac{{\sqrt 3 }}{4} \times 6 \times 6 = 72\sqrt 3 {\text{ c}}{{\text{m}}^2}$$