How to Find the Area of a Sector: Formula and Step-by-Step Guide

area of a sector formula

A = 1/2r²θ with angle in RADIANS

The formula for the area of a sector is:

A = (θ/360) * π * r^2

where:
– A is the area of the sector
– θ is the central angle of the sector, measured in degrees
– r is the radius of the circle that the sector is a part of

To use the formula, you need to know the central angle and the radius of the sector.

First, you need to convert the central angle from degrees to radians. You can do this by multiplying the angle measure by π/180.

Then, you can plug in the values into the formula and simplify.

For example, let’s say we have a sector with a central angle of 60 degrees and a radius of 5 cm.

First, we convert the central angle to radians:

60 * π/180 = π/3

Then, we can plug in the values into the formula:

A = (π/3/360) * π * 5^2
A = (1/6) * π * 25
A = (25/6) * π

So the area of the sector is (25/6) * π, which is approximately 13.1 square units.

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