Question

Please help me out!! :)

Answer 1

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)

`10 \sqrt3cm=10 * 1.732=17.32 cm`

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
`10 \sqrt 3` cm. So the area of one equilateral triangle is:

`(\sqrt 3)/(4) * (a)^2`

Where, 'a' is the side length of the equilateral triangle.

Therefore, area
`= (\sqrt 3)/(4) * (10 \sqrt3)^2= (\sqrt 3)/(4) * 100 * 3=75 \sqrt3` 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
`=6 * 75 \sqrt 3=450 \sqrt 3 cm^2`.