For math, I have to find the area of a hexagon when all I know is that each side equals x. I also know that I have to use 3 thereoms. HELPP!

2 answers

make a sketch.
from the centre draw lines to each of the 6 vertices. This will give you six equilateral triangles with sides x.
Let's concentrate on one of these
Drawing a height "h" in one of these triangles will give us a right-angled triangle of base x/2, height of h, and hypotenuse of x
so (x/2)^2 + h^2 = x^2
x^2/4 + h^2 = x^2
.
.
h = (√3/2)x

so the area of one triangle = (1/2)(x)√3/2)x
= (√3/4)x^2
but we have 6 of these, so
total area
= 6((√3/4)x^2)
= (3√3/4)x^2
messed up the last, line should say
(3√3/2)x^2
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