Solves polygon area inscribed in a circle\[P_a=\frac{1}{2}n\cdot a\cdot r_i \]
The area of a regular polygon inscribed in a circle refers to the total amount of space occupied by the polygon when each of its vertices touches the circumference of the circle. This concept is commonly used in geometry to calculate and understand the relationship between the polygon and the circle it is inscribed in.
To calculate the area of polygon, consider the following factors
Radius of the circle
In-circle area
Area of a regular polygon inscribed in a circle
To calculate the area of a regular polygon inscribed in a circle, you can use the formula:
Area = (n (r^2) sin((360°) / n)) / 2
where n is the number of sides of the polygon, r is the radius of the circle, and sin() is the sine function.
Alternatively, you can also calculate the area by subtracting the area of the incircle from the area of the circle. The incircle's area can be calculated using the formula:
Incircle Area = (π * (r^2)) / 2
By subtracting the incircle area from the circle area, you will obtain the area of the polygon.