Area of a segment

How to calculate the area of a segment

0
2020
Area of a segment

The area of a segment can be calculated using the following formula

If using degrees:

A = (r2 ÷ 2) x ((Π ÷ 180 x Θ) – sin Θ)

If using radians:

A = (0.5 x r2) x (Θ – sin Θ)

Where:

A = Area

r = Radius

Π = Pi  (3.14)

Θ = Angle

0.5 = A constant

180 = A constant

Example (In Degrees)

You’ve been asked to calculate the area of a sector when the radius of the circle is 5m and the angle is 120 degrees.

A = (r2 ÷ 2) * ((Π ÷ 180 * Θ) – sinΘ)

A = (52 ÷ 2) * ((Π ÷ 180 * 120) – sin120)

A = (12.5) * ((Π ÷ 180 * 120) – sin120)

A = (12.5) * ((0.017453 * 120) – sin120)

A = (12.5) * ((0.017453 * 120) – sin120)

A = (12.5) * ((2.0944) – 0.866025)

A = (12.5) * (1.22837)

A = 15.35m2

Example (In Radians)

You’ve been asked to calculate the area of a sector when the radius of the circle is 5m and the angle is 2.094 radians. (Remember! put your calculator in radians)

A = (0.5 x r2) x (Θ – sin Θ)

A = (0.5 x 52) x (2.094 – sin 2.094)

A = (0.5 x 25) x (2.094 – sin 2.094)

A = (12.5) x (2.094 – sin 2.094)

A = (12.5) x (2.094 – 0.86622)

A = (12.5) x (2.094 – 0.86622)

A = (12.5) x (1.22778)

A = 15.35m2

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