Jake5667

Area = (sqrt(3)/4) * side^2

Substituting "a" for the side length, we have:

Area(XYZ) = (sqrt(3)/4) * a^2

To find the area of the circle, we need to calculate the radius (R). Since OX is the altitude of triangle OYZ, and triangle XYZ is equilateral, we can use the formula for the altitude of an equilateral triangle:

OX = (sqrt(3)/2) * a

Since OX = R, we have:

R = (sqrt(3)/2) * a

Now, let's find the area of the circle. The area of a circle is given by the formula:

Area(circle) = pi * radius^2

Substituting the value of the radius (R), we get:

Area(circle) = pi * ((sqrt(3)/2) * a)^2 = (3pi/4) * a^2

Therefore, the area of the circle is (3pi/4) * a^2.