MHB Find the area of the shaded region in terms of pi.

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The area of a full circle is calculated using the formula πr². For a sector, the area is determined by the fraction of the circle's angle, leading to the formulas (120/360)(πr²) and (270/360)(πr²). With a radius of 12 meters, the area of the first sector is confirmed as 12π, while the area of the second sector is calculated as 108π. The final confirmation of the area for the second sector is expressed as A=(1/2)(12 m)²(3π/2)=108π m². The calculations for both sectors are verified as correct.
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So far i have.

12) area of full circle is πr²
area of sector is (120/360)(πr²) or 12π

13) same
area is (270/360)(πr²)

Am i correct?

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#12 is correct ... finish #13
 
Im assuming 12m is the radius so \frac{270}{360}pi×12squared=108 pi
Am i correct?
 
$$A=\frac{1}{2}r^2\theta=\frac{1}{2}(12\text{ m})^2\frac{3\pi}{2}=108\pi\text{ m}^2\quad\checkmark$$
 

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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