This is known as the Sector Area Formula.

[susanto3311]

hello guys..

how to figure it out this below problem, find area of circle

please, see my picture..

thanks...

susanto3311

 

[MarkFL]

What are your thoughts here on what you should do?

 

[susanto3311]

i confused about 240...how to elaborate with commonly area formula?

 

[MarkFL]

If $240^{\circ}$ is outside the sector whose area we want, then what angle is inside, and then what portion of the whole is this?

Can we generalize from this to get a formula for the area of a circular sector?

 

[susanto3311]

can you make to me more simple, i think be illustrated with my problem sample.

 

[MarkFL]

A circle "encloses" $360^{\circ}$...if $240^{\circ}$ is outside the sector we want, how much is inside?

 

[susanto3311]

hi Mark..

360-240 = 120, then...how to elaborate?...

 

[MarkFL]

What portion of 360 is 120?

 

[susanto3311]

What portion of 360 is 120?

=120/360=0.333, so...

 

[MarkFL]

Actually, we have:

\(\displaystyle \frac{120}{360}=\frac{1}{3}\)

So, what portion of the area of the whole circle do you suppose the area of the sector would be?

 

[susanto3311]

Actually, we have:

\(\displaystyle \frac{120}{360}=\frac{1}{3}\)

So, what portion of the area of the whole circle do you suppose the area of the sector would be?

hi Mark, finally
i think like this :

It's true, Mark?

 

[MarkFL]

Yes, since 1/3 of the total angle within the circle is subtended by the sector, then its area is 1/3 of the whole circle. So, we could generalize and state that if the angle subtended within two radii of a circular sector is $\theta$ (given in radians) then the area $A$ of the sector is:

\(\displaystyle A=\frac{\theta}{2\pi}\cdot\pi r^2=\frac{1}{2}\theta r^2\)