Area - triangles, quadrilaterals, compound shapes

problem

Bicentric Quadrilaterals

Age

14 to 16

Challenge level

Investigate the properties of quadrilaterals which can be drawn with a circle just touching each side and another circle just touching each vertex.
problem

Halving the Triangle

Age

16 to 18

Challenge level

Draw any triangle PQR. Find points A, B and C, one on each side of the triangle, such that the area of triangle ABC is a given fraction of the area of triangle PQR.
problem

Another Triangle in a Triangle

Age

16 to 18

Challenge level

Can you work out the fraction of the original triangle that is covered by the green triangle?