Hi,

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 .