Formula for the area of an equilateral triangle with side length
a
is
A
t
=
√
3
4
⋅
a
2
Let
2
x
be the side length of the equilateral triangle,
given that area of the equilateral
A
t
=
2
units
2
⇒
A
t
=
√
3
4
⋅
(
2
x
)
2
=
√
3
4
⋅
4
x
2
=
2
⇒
x
2
=
2
√
3
units
2
A regular hexagon can be divided into 6 congruent equilateral triangles, as shown in the figure.
given that the equilateral triangle and the regular hexagon have equal perimeter,
⇒
side length of the hexagon
=
3
⋅
2
x
6
=
x
units
⇒
area of the regular hexagon
=
A
h
=
6
⋅
√
3
4
⋅
x
2
⇒
A
h
=
6
⋅
√
3
4
⋅
2
√
3
=
3
units
2
