MHB How do you calculate the area and arc length of region ABCD using given values?

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To calculate the area of region ABCD, the formula used is A = (θ/2)(R² - r²), where R = 3k, r = 2k, and θ = 3/4. Substituting these values into the formula allows for solving for k. The arc length difference is determined using the formula Δs = θ(R - r). By applying the given values, the calculations for both area and arc length can be completed. This approach effectively provides the necessary methods for determining the area and arc length of the specified region.
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area of region ABCD ...

$A = \dfrac{\theta}{2}\left(R^2-r^2\right)$

you have $R = 3k$, $r=2k$, and $\theta = \dfrac{3}{4}$

... proceed to solve for $k$

also, arc length difference is $\Delta s = \theta(R - r)$
 

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