How to Find the Area of Major and Minor Segments of a Circle?

Circle can be defined as a line that has curved shape and all points on line are at fixed distance from center. Now we will see how to find the area of major and minor segments of a Circle. Formula to find the area of Major Arc is given as:

Area of major arc of circle = R² / 2 (π / 180 C – sin C), here value of ‘C’ stands for central angle that are given in degrees, value of ‘R’ stands for Radius of Circle, value of ‘π’ is 3.14, ’sin’ is the Trigonometry sine function.

Now we will see formula to find the area of Minor Arc which is given as:

Area of minor arc of a circle = 1 / 4 [π * r² * angle / 360 – chord (r² …..Upon 4)] or

Area of minor arc of a circle = (θ / 360⁰) * (pi) * r² or

Area of minor arc of a circle = area (circle) – area (major segment). We can find the area of minor arc of a circle using all these three formulas. It will be clear with help of example:

Suppose we have total area of circle as 50 inch², radius of circle is 3.5 inch and central angle of circle is given as 115⁰. Find the area of major and minor arc of circle.

First see the case of area of major arc of a circle. Formula to find the area of major arc of circle is given as:

Area of major arc of circle = R² / 2 (π / 180 C – sin C), put all values in the formula. On putting the values we get:

Area of major arc of circle = (3.5)² / 2 (π / 180 * 115⁰ – sin 115⁰), on further solving we get area of major arc of circle as 6.7 inch².

Now see how to find the area of minor arc of circle.
Area of minor arc of a circle = 50 – 6.7 = 43.3 inch². In this way we can find the area of major and minor arc of circle.