Question

find the area of a regular hexagon whose one side measures 4 cm​

Answer 1

Answer:

⟹Let ABCDEF be the regular hexagon.

⟹Let O be its centre which is the point of intersection of its diagonals AD, BE and CF.

⟹Then, the regular hexagon is divided into six equilateral triangles each of side 4 cm.

Area of equilateral Δ OAB ⟹

$( \dfrac{ \sqrt{3} }{4} \times {4}^{2} ) {cm}^{2} = 4 \sqrt{3}$cm²

Area of hexagon ABCDEF ⟹ 6 × Area (Δ OAB)

⟹ $(6 \times 4 \sqrt{3} )$cm²

⟹ $24 \sqrt{3}$cm²

Hence, the area of a regular hexagon whose side is 4 cm is $24 \sqrt{3}$cm²