Here is drawn regular hexagon. It consists of 6 equilateral triangles with side length [tex] a=10\sqrt{3} [/tex] cm. The area of equilateral triangle is
[tex] A_{triangle}=\dfrac{a^2\sqrt{3}}{4} [/tex].
Substitute [tex] a=10\sqrt{3} [/tex] into the previous formula:
[tex] A_{triangle}=\dfrac{(10\sqrt{3} )^2\sqrt{3}}{4} =\dfrac{300\sqrt{3}}{4}=75\sqrt{3}[/tex].
Then
[tex] A_{hexagon}=6A_{triangle}=6\cdot 75\sqrt{3} =450\sqrt{3}=779.4228=779.4 [/tex] sq. cm.
Answer: [tex] A_{hexagon}=779.4 [/tex] sq. cm.
