The two largest circles below have a radius of 6 units and are divided into cong...

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November 2022 1 5 Report

The two largest circles below have a radius of 6 units and are divided into congruent arcs. Verify that each of the 24 regions has the same are if OA=3√2 and OB=6

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jamelbenibrahim

Find the area of each regions of a circles.

The first circle is composed of 12 identical parts that has an area of

$A_{ \frac{1}{12} } = \frac{A}{12 } = \frac{\pi {r}^{2} }{12} = \frac{\pi {(6)}^{2} }{12} = \frac{36\pi}{12} = 3\pi \: {unit}^{2}$

The second circle is also 12 parts but 6 of them is identical and the other six is identical too.

The area of the firs 6 region is

$A_{ \frac{1}{6} a} = \frac{A_{OA}}{6} = \frac{\pi {r_{OA}} {}^{2} }{6} = \frac{\pi(3 \sqrt{2} ) {}^{2} }{6} = \frac{18\pi}{6} = 3\pi \: {units}^{2}$

The other 6 parts has an area of

$A_{ \frac{1}{6} b} = \frac{\pi \: r_{ob} {}^{2} } {2} = \frac{\pi {(6)}^{2} }{6} - 3\pi = \frac{ 36 \pi}{6} - 3\pi = 3\pi$

Since, each area of 24 regions are equal to

$3\pi$

Then, they are same or identical or equal area which is

$3\pi$

atpoffgun3 thankyou po

atpoffgun3 salamat talaga

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