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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?

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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.

From All Corners

Stage: 4 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3
Straight lines are drawn from each corner of a square to the mid points of the sides which are opposite, as shown.

Express the area of the octagon as a fraction of the area of the square.