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Giant Holly Leaf
Find the perimeter and area of a holly leaf that will not lie flat (it has negative curvature with 'circles' having circumference greater than 2πr).
Quadarc
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.
Get Cross
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 Short Challenge Level:
At the corner of a cube, circular arcs are drawn as shown.
What fraction of the surface area of the cube is shaded?
You can find more short problems, arranged by curriculum topic, in our short problems collection.
Sine, cosine, tangent. Regular polygons and circles. Fractions. 2D shapes and their properties. Circle properties and circle theorems. Pythagoras' theorem. Area - circles, sectors and segments. Creating and manipulating expressions and formulae. Mathematical reasoning & proof. Surface and surface area.
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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.