# Fraction Problem #2

Two congruent regular octagons intersect as shown.

What fraction of the left octagon does the red shape encompass?

What fraction of the combined black shape does the blue shape encompass?

## 6 thoughts on “Fraction Problem #2”

1. workedgechaos says:

Right, I give up. A little help?

2. workedgechaos says:

Ignore my last comment, I’ve just realised something very obvious. Doh!

It’s sin45 or 1/√2 – I’m really embarrased.

• workedgechaos says:

That’s for the red triangle anyway.

• The area of the red triangle has to be less than half that of the octagon. 1 / sqrt2 is more than a half. What was your method?

You need to construct a formula for the area of the triangle and the area of the octagon using a single constant. e.g. the diameter of the circle you could inscribe the octagon into, or the radius, or, most likely (and easiest I think), the length of a side of the octagon.

• workedgechaos says:

I realise I’ve made a mistake. I’ve tried to find the area of the octagon the used the sine rule to find the area of the triangle. But I’ve spotted a mistake in the maths. I’ll have another go.

3. cornishhalfy says:

I get (1-3sqrt2)/3 any good?