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The area is approximately ##86.6 cm^2##.

As this hexagon is regular you can divide it into ##6## triangles.

Please note that all those triangles are isosceles. All angles of the hexagon are ##120##.

As you see in the picture each of those 6 big triangles can be divided into two small triangles with the angles ##30## ##60## and ##90## and we know the length of one of the sides: ##a = 5 cm##.

To compute the area of the small right angle triangle you need just the length of ##b##.

This you can do with ##tan##:

##tan (30) = b/a##

##b = 5 cm * tan(30) = 2.88675134595… cm##

This means that the area of the small right angle triangle is

##A_t = (b * a)/2 = (5 cm * 5 cm tan(30))/2 = 25/2 tan(30) cm^2 = 7.21687836487… cm^2##

There are ##12## equal triangles so the area of the whole hexagon is

##A = 12 * A_t = 6 * 25 tan(30) cm^2 = 86.6025403784… cm^2 ##

Hope that this helped!

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