Question 18511
Let ABC be the equilateral triangle whose verticle lie on the circle with a radius of 2cm and "O" as the center.

AH the perpendicular from A to BC is the altitude

In an equilateral triangle the altitude is also the median.

So O is also the centroid of the triangle 

So ---->OH/AO = ½
	
OH= OA/2 = 2/2 = 1cm

AH=2+1=3cm

In the triange OCH

OC=2cm


OH=1cm

apply the pythagorean theorem

OC^2= OH^2 + HC^2
or
HC^2 =OC^2 - OH^2

=2^2-1^2

=4-1=3
HC = √3

The side of the triangle BC =2HC = 2√3

The area of the triangle:

AH X BC
-------
   2
= 2 X 2√3
 --------
    2

= 4√3
 -----
   2
Area of the triangle is 2√3 cm^2