Question

A regular hexagon has a perimeter of 60 m. Find its area. Leave your answer in simplest radical form

Answer 1

Imagine the hexagon as 6 equilateral triangles stuck together.
The outside "boundary" is 60 m, so each of the six triangles has 10-inch sides.
The only way I know how to get the altitude(height) of each triangle is to bisect each triangle and use the pythagorean theorem.
So, I know the hypotenuse is 10, and the base is half that, so 5
a² + b² = c²
a² + 5² = 10²
a² + 25 = 100
a² = 100-25
a² = 75
a = 75-² , so the altitude, a is the square root of 75, or 8.66 something.

So now we have 12 pieces, each with a=8.66 and b=5
area of triangle = half of the altitude times the base or A=ab/2
8.66``(5)=43.30something
divide by 2 and multiply by 12 gets you the total area of the hexagon: 259.80something.

Round off and the answer is

260 square meters

Answer 2

have a good one hope it helped :)

Answer 3

Thanks!

Answer 4

yeah np WELCOME TO OPENSTUDY @antc321