Question

Let abcdef be a regular hexagon.What is the ratio of area of triangle ace to area of hexagon abcdef

Answer 1

Answer:

Let the sides of the regular hexagon ABCDEF be s.

The area of ABCDEF = area of 6 equilateral triangles of side, s = 6[s*s*sin 60]/2 = 2.598076211 s^2 sq units.

Applying cosine for the triangle ABC,

AC^2 = AB^2+BC^2–2*AB*BC*cos 120

= s^2+s^2–2s^2*(-0.5) = s^2+s^2+s^2 =3s^2

or AC = s√3

The area of ACE, which is an equilateral triangle of side, s√3

= (s√3*s√3*sin 60)/2 = 1.299038106s^2 sq units which is half the area of the hexagon.

So the ratio of the area of triangle ACE to hexagon ABCDEF is 1:2. Answer.

Answer 2

Answer:

the ratio of area of triangle ace to area of hexagon abcdef is :- 1:2