Area of a regular dodecagon?

A regular dodecagon is inscribed in a circle whose radius is given. What’s its area?

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[googelman]

you could still use the formula (apothem * perimeter)/2 but finding the perimeter would take a bit more work as you would have to do trig stuff

[IMGMYT]

Bro I need a unreal engine 5 for me to simulate this in my mind

[im.rishabh_ofc]

And if we increase the number of sides and make a infinite sided polygon just like this one its area will be πr²

[valentinnovo]

Well the area of the yellow shape should be 100 a.u as the black dodecagon has an area of 300 a.u

[amberbaloch]

Can anybody explain me in simple language

[ancientstraits]

just say the area is 25pi. It barely makes a difference at that point

[mintyjuicey]

100 fr fr since if we use the equation given we would have the hollowed part as 3*sqrt(10)=300 then if the full shape is a square, we have sqrt(10*2)=400 and minus them together, we get 100