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Prove that the area of a sector with central angle φin a circle of radius ris given by A=12φr2.

Short Answer

Expert verified

The area of a sector of a circle is A=12φr2which is formulated by using the property of proportionality os central angle and the area.

Step by step solution

01

Step 1. Given Information

The central angle of the sector isφ.

02

Step 2. Use the proportionality property

  • It is known that the area of a circle is A=πr2.
  • Also, the area of a sector of a circle is proportional to the central angle.
  • The central angle of the entire circle is 2π.
  • So, the formula of the sector is calculated as shown below:

A'=φ2ππr2=12φr2

  • So, the area of the sector of a circle is12φr2.

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