Two sectors of a circle of radius 12 overlap as shown, with P and R as the centers of the respective circles. Determine the area of the shaded region.
+2668 Let the intersection point directly above \(P\) as \(A\), and let the point that is to the left of \(P\) be \(B\)
The area of \(\triangle ABP = 12 \times 12 \div 2 = 72\)
The area of the circular region \(ABP\) is \( {1 \over 4} \times 12^2 \times \pi = 36 \pi \)
Now, note that the area of the shaded region is \(2 (\text{circular region of ABP} - \triangle ABP) \)
Substituting what we know, we find that the area of the shaded region is \(\color{brown}\boxed{72 \pi - 144}\)
+2668 Let the intersection point directly above \(P\) as \(A\), and let the point that is to the left of \(P\) be \(B\)
The area of \(\triangle ABP = 12 \times 12 \div 2 = 72\)
The area of the circular region \(ABP\) is \( {1 \over 4} \times 12^2 \times \pi = 36 \pi \)
Now, note that the area of the shaded region is \(2 (\text{circular region of ABP} - \triangle ABP) \)
Substituting what we know, we find that the area of the shaded region is \(\color{brown}\boxed{72 \pi - 144}\)
