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A white cross is placed symmetrically in a red disc with the central square of side length sqrt 2 and the arms of the cross of length 1 unit. What is the area of the disc still showing?
Age 14 to 16 Challenge Level:
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 $PQRS$.
Creating and manipulating expressions and formulae. Circle properties and circle theorems. Area - circles, sectors and segments. Visualising. Sine, cosine, tangent. 2D shapes and their properties. Sine rule & cosine rule. Regular polygons and circles. Pythagoras' theorem. Angles - points, lines and parallel lines.
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NRICH is part of the family of activities in the Millennium Mathematics Project.
NRICH is part of the family of activities in the Millennium Mathematics Project.