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# How do I find the area of this sector?

What is the area of the sector with a central angle of 45d and radius 23cm?

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- Anonymous1 decade agoFavorite Answer
Given a sector with a radius of r and subtended by an angle of θ (in radians), the area is:

A = (1/2)r^2θ.

Since r = 23 and θ = 45° = π/4, the sector has area:

A = (1/2)(23)^2(π/4) = 529π/8 cm^2.

I hope this helps!

- AlbundyLv 41 decade ago
You can convert to rectangular coordinates to see the shape you are forming.

To convert use>

x=r cos 45, 23*cos45=16.263 value of x=base.

y=r sin 45, 23*sin45= 16.263 value of y=high

Now you have a triangle of base 16.263,high of 16.263 and a diagonal of 23.

Area of that triangle=.5*b*h=.5*16.623^2=132.25cm^2.

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