I am struggling with a question in the guesstimate section. Although you did a good job of clarifying I am still a bit confused as math isn’t my strongest suit. The question is:
p. 52, Q.20: In the figure above A is the centre of the circle, A and D lie on BF and CE respectively, and B, D, F, and G lie on the circle. If BC=3, and DG bisects BF, what is the total area of the shaded regions?

I am just wondering, how you would go about calculating the area of the shaded region in detail.


OK, so here are the key things: BCEF is a rectangle, BF and DG are diameters, and AD  = 3 just like BC does. So the circle has a radius of 3.

Triangle GEC has a base and a height of 6. Therefore, the smaller, similar triangle with a height of GA has a base and a height of 3.

The shaded region will be the area of half the circle minus the area of that small triangle. That’s \dfrac{\pi 3^2}{2}-\dfrac{1}{2}(3)(3) = \dfrac{9\pi - 9}{2}.

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