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A point P is selected anywhere inside an equilateral triangle. What can you say about the sum of the perpendicular distances from P to the sides of the triangle? Can you prove your conjecture?

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Areas and Ratios

What is the area of the quadrilateral APOQ? Working on the building blocks will give you some insights that may help you to work it out.

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Six Discs

Six circular discs are packed in different-shaped boxes so that the discs touch their neighbours and the sides of the box. Can you put the boxes in order according to the areas of their bases?

Diagonals for Area

Stage: 4 Challenge Level: Challenge Level:1

This only uses the result that the area of a triangle is half the base times the height but you need to consider different cases according to whether the quadrilateral is convex or concave.