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Areas and Ratios

Do you have enough information to work out the area of the shaded quadrilateral?

Pent

The diagram shows a regular pentagon with sides of unit length. Find all the angles in the diagram. Prove that the quadrilateral shown in red is a rhombus.

Golden Ratio

Solve an equation involving the Golden Ratio phi where the unknown occurs as a power of phi.

Reductant Ratios

Age 16 to 18 Challenge Level:
The relative atomic masses of iron and oxygen are $56$ and $16$ respectively