Tilting Triangles

A right-angled isosceles triangle is rotated about the centre point of a square. What can you say about the area of the part of the square covered by the triangle as it rotates?
Exploring and noticing Working systematically Conjecturing and generalising Visualising and representing Reasoning, convincing and proving
Being curious Being resourceful Being resilient Being collaborative


A right-angled isosceles triangle whose two equal sides are 2 units in length is attached at its right-angled vertex to the centre of a square of side 2 units and rotated about this centre point.



What can you say about the area of the part of the square covered by the triangle as it rotates?

What happens to this area if the triangle is reduced in size so that its two equal sides are $ \sqrt 2 $ units?

What happens if the triangle is further reduced in size?