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?

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Right, I give up. A little help?

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

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

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.

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.

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