Question

In the figure above, ABCDEF is a regular hexagon.
If area of AACE is 100/3 cm, what is the area of
the hexagon?​

Answer 1

As area of tri 100√3

so each side of triangle ACE

=200cm

so area of rect ACDF

=AC*AF=100*AF

and angle BAC=BCA

=29°+(2/3)°

So height of triangle ABC/half AC

=height of tri/100

=tan 29.66°=0.5694

so ht of triangle=56.94cm

Hence area of tri ABC

=56.94*100......(1)

Also AF=AB

=√(56.94sq+100sq)

=√(3242+10000)

=√13242

=115.07

so area of rect ACDF

=115.07*AC

=115.07*200......(2)

So area of hex

=area of rect ACDF+(2*area of tri ABC)

=(115.07*200)+(56.94*200)

=200*(115.07+56.94)

=200*42

8400 sq cm ANSWER