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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?

Of All the Areas

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

These diagrams might help you to work out the areas of the tilted triangles. For each image, we have included an image from the geoboard environment as well as an accurate version:

Here is another diagram which might help you to find another method to calculate the areas: