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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?

Areas of Parallelograms

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2
Try drawing a rectangle around the parallelogram. If you can work out the area of the rectangle and the areas of the parts of the rectangle outside the parallelogram, then you should be able to find the area of the parallelogram.

Don't forget that you can break up complicated shapes into simpler small shapes (such as triangles and rectangles) whose areas are easier to find.