See e.g. The Daily Express.
1. Here's the basic question. Let's assume side length is 10, for sake of argument.
Sides are all the same length r = 10, so it is an isosceles triangle and angles = 60 deg.
Fold it in half (middle triangle) and the bottom side is half r = 5.
The vertical side is the square root of r^2 - 1/2 r^2 = square root of 3/4 r^2 = square root of 75.
The area of the triangle on the right (or on the left, for that matter) = base x height x 1/2
= 5 x square root of 75 = about 43 in old money.
Angle of the triangle on the right where it touches the center of the circle = 120 deg. (needed for 3. above)
= about 62 in old money.
= 100 pi - 400/3 pi + 20 x square root of 75
= - 100/3 pi + 20 x square root of 75
= which is about 68.5 in old money.
Looks about right, that's a bit more than one-fifth of the area of the circle (which is about 314).