A square is dissected to form three triangles and a quadrilateral. What fraction of the square is each part?
A square is divided into three triangles and a quadrilateral by drawing a diagonal and a line joining one of the other vertices to the midpoint of a side. TI-Nspire calculates the area of each part of the square and poses a question: what fraction of the area of the square is the area of each part?
Varying the size of the square allows students to collect data that can be plotted as a scattergraph. This leads to a derivation of the fractions for each part.
A separate problem allows the result to be checked using coordinate geometry and algebra.
Finally there is an extension problem that allows students to work towards a generalisation of what happens when, rather than the midpoint, the side of the square is divided in the ratio r:1.