The area of an equilateral triangle inscribed in a circle of radius c is

The area of an equilateral triangle inscribed in a circle can be calculated using the radius of the circle. For an equilateral triangle inscribed in a circle of radius \( c \), the formula for the area \( A \) is given by:

Area Formula

The area \( A \) can be expressed as:

A = (3√3/4) * c²

Explanation of the Formula

• Radius (c): This is the distance from the center of the circle to any vertex of the triangle.
• Equilateral Triangle: All sides and angles are equal, which simplifies the calculations.
• Inscribed Triangle: The triangle fits perfectly within the circle, touching it at all three vertices.

Example Calculation

If the radius \( c \) is 2, the area would be:

A = (3√3/4) * (2)² = (3√3/4) * 4 = 3√3

This formula allows you to find the area of any equilateral triangle inscribed in a circle, just by knowing the radius.