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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).

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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.

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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?

Two Shapes & Printer Ink

Age 14 to 16 Challenge Level:
  • The main task for the student here is to identify and accurately describe the geometric properties possessed by these shapes.

  • Then to make that identification the basis for calculation and interpretation.