1. What is the area of the blue shape?
½(25π - 4π - 9π)
= 6π 6m 4m
Trying this with some real examples should reinforce the idea that can be demonstrated algebraically – that equal semicircular bites give the greatest area – half of the original semicircle. The equation is a quadratic with a maximum in the middle.
What is the area of
the blue shape?

2. What is the area of the blue shape?
½(25π – 6.25π – 6.25π)
= 6.25π 5m 5m
What is the area of
the blue shape?

3. What is the area of the blue shape?
½(¼π – x2/4 π – (1 – x)2/4 π)
= π/8 (1 – x2 – (1 – x)2)
= π/8 (1 – x2 – 1 + 2x – x2)
= π/4 x(1 – x)
x m
(1 – x) m
Simplifies to a quadratic which crosses the axes at 0 and 1, having its maximum therefore at 0.5 (halfway across the circle).
What is the area of
the blue shape?