Question

AREAS OF REGULAR POLYGONS HELP?

Answer 1

Here is drawn regular hexagon. It consists of 6 equilateral triangles with side length
`a=10√(3)` cm. The area of equilateral triangle is

`A_(triangle)=(a^2√(3))/(4)`.

Substitute
`a=10√(3)` into the previous formula:

`A_(triangle)=((10√(3) )^2√(3))/(4) =(300√(3))/(4)=75√(3)`.

Then

`A_(hexagon)=6A_(triangle)=6\cdot 75√(3) =450√(3)=779.4228=779.4` sq. cm.

Answer:
`A_(hexagon)=779.4` sq. cm.