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Zach · Q20

Geometry

Given that CBCB is an arc formed from the circle of radius aa centred at AA, and ABAB and ACAC are defined similarly, what is the area of the shape ABCABC in terms of aa? Diagram for question 20

Aa22(π−3tan⁡π6)\frac{a^2}{2}\left(\pi-3\tan\frac\pi6\right)
Ba22(π−3tan⁡π3)\frac{a^2}{2}\left(\pi-3\tan\frac\pi3\right)
Ca22(π−3sin⁡π6)\frac{a^2}{2}\left(\pi-3\sin\frac\pi6\right)
Da22(π−3sin⁡π3)\frac{a^2}{2}\left(\pi-3\sin\frac\pi3\right)
E3a2πtan⁡(π6)3a^2\pi\tan\left(\frac\pi6\right)

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