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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?

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? Correct Answer 72√3

Area of equilateral ΔAFP = √3/4 × 36 = 9√3 cm2

Area of quadrilateral ABOF = 2 × Area of ΔAFP = 18√3 cm2

Similarly, Area of quadrilateral DCOE = 2 × Area of ΔEDS = 18√3 cm2

Area of Shaded region = Area of quadrilateral ABOF + Area of quadrilateral DCOE) + 4 × Area of equilateral ΔAFP

∴ Area of Shaded region = 18√3 + 18√3 + 36√3 = 72√3 cm2

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