Math Q!!!!!

[dfymarine]

Find the shaded area!


the radius of the circle is 1

and the short side of triangle is 1


please tell me the quickest way to solve it!!!! thanks!

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[UCB05]

Find the shaded area!


the radius of the circle is 1

and the short side of triangle is 1


please tell me the quickest way to solve it!!!! thanks!

the inner shape is a rectangle correct? It took me a bit of thinking. there could be a faster way than mine. figure out the magnitude of the inner angle of the shaded region. To do that, use some geometry to find the angle of the outer region. Equilateral triangle is 60/60/60, inside angle is half of the remainder (sum of the angles around the center is 60/60/120/120). Once you know that that angle is 120 degrees, the area of that region of the circle (shaded and white region) is equal to 120/360 or 1/3 the total area of the circle, which is pi(1^2). from that subtract the area of the white region: (pi/3 - √3/4) is that the correct answer?

 

[dfymarine]

yes that's the correct answer

but, it took me so long to solve it >.<

 

[UCB05]

yes that's the correct answer

but, it took me so long to solve it >.<

Maybe your best bet then is to skip it and come back to it later if you're short on time.