We need to find the area of the regular polygon as shown in the image.
Now in a regular hexagon the line joining the center and the vertex of a hexagon have the same length as the length of each side. (Refer the attached image)
[tex]10 \sqrt3cm=10 \times 1.732=17.32 cm[/tex]
A regular hexagon is made up of 6 equilateral triangles inside which means all the sides are of the same length.
Now, we know that the length of a side of an equilateral triangle is [tex]10 \sqrt 3[/tex] cm. So the area of one equilateral triangle is:
[tex]\frac{\sqrt 3}{4} \times (a)^2[/tex]
Where, 'a' is the side length of the equilateral triangle.
Therefore, area [tex]= \frac{\sqrt 3}{4} \times (10 \sqrt3)^2= \frac{\sqrt 3}{4} \times 100 \times 3=75 \sqrt3[/tex] square centimeters.
Now that we have the area of one equilateral triangle and there are 6 of them in a regular hexagon we can find the area of hexagon.
So, the area of given regular polygon is [tex]=6 \times 75 \sqrt 3=450 \sqrt 3 cm^2[/tex].
