Fraction Problem #2

octagon fraction

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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6 thoughts on “Fraction Problem #2

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

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

      • 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.

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