Categories
Intermediate

The pentangle flower

Multicoloured pentangle in a red circle. Rhombuses form two levels of petals growing outward, forming a decagon. Show that the opposite sides of the two interleaved pentagons are equal in pairs and also equal and parallel to the sides of the pentangle.

Categories
Intermediate

The inner diamond

A triangle with side lengths a and b and an inscribed rhombus. What is the blue fraction in terms of a and b?

Categories
Beginner

The parquet floor

A unit rhombus is surrounded by four congruent parallelograms. All five quadrilaterals have equal area. What are the parallelogram sides x and y?