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At a Glance

The area of a regular pentagon looks about twice as a big as the pentangle star drawn within it. Is it?

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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?

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Given a square ABCD of sides 10 cm, and using the corners as centres, construct four quadrants with radius 10 cm each inside the square. The four arcs intersect at P, Q, R and S. Find the area enclosed by PQRS.

Of All the Areas

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

You may find it useful to take a look at More Isometric Areas.
These diagrams might help you to work out the areas of the tilted triangles. 

The top diagrams show how drawing a non-tilted triangle around the tilted triangle could help you to find the area of the tilted triangle.

Area of tilted triangle = Area of blue triangle - Area of 3 green triangles

This diagram show some lines that can be drawn inside the tilted triangle:

Area of tilted triangle = Area of pink triangle + Area of 3 blue triangles