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For a square of side a, the area is simple: a2. The perimeter is 4a. How do you deal with a circle, of diameter a? It's obviously less than a2. It turns out to be pi/4 times a2. Or pi times radius squared where pi has been worked out to be 3.1415..... As for angle, for lots of applications it appears a good way of measuring angle by using the length of a piece of circumference of a circle divided by the radius. The units for this is radians. A length of circumference equal to the circle radius gives an angle of 1 in these units when you draw straight lines from the ends of this bit of circumference to the centre. So the whole way around the circle (360o) then is 2.pi.r divided br r, radians, which is just 2 pi radians.

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Q: Why pi in area and angle?
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