MHB Find the area of sector in a circle in terms of pi. (Geometry)

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To find the area of a sector in a circle, the formula involves multiplying the fraction of the circle represented by the angle by the area of the entire circle. In this case, the angle of 270 degrees simplifies to 3/4 when divided by 360 degrees. The area \(A\) is calculated as \(A = \frac{3}{4}\pi r^2\). With a radius of 12 meters, substituting into the formula gives an area of 108π. The final answer of 108π is confirmed as correct.
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So far i have 270/360× (pi)r^ i don't know what to do next please help.
 

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I would first reduce:

$$\frac{270^{\circ}}{360^{\circ}}=\frac{3}{4}$$

And so we now have the area \(A\):

$$A=\frac{3}{4}\pi r^2$$

Can you identify the radius \(r\) of the circle from the diagram?
 
The radius i believe is 12m so when i plug in your formula i get 108pi as the answer. Am i correct?
 
Yes, 108\pi is correct.
 

Thread 'Area of Overlapping Squares'

Here is a little puzzle from the book 100 Geometric Games by Pierre Berloquin. The side of a small square is one meter long and the side of a larger square one and a half meters long. One vertex of the large square is at the center of the small square. The side of the large square cuts two sides of the small square into one- third parts and two-thirds parts. What is the area where the squares overlap?
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