triangle areas

ways to see that a triangle is half a rectangle

in these growing sequence of triangles
what happens to the areas?

when students appreciate that all the areas are the same (for each strip) they can be asked to justify this by indicating which base and height they have used to make their calculation

these tasks involve Pick's theorem and can involve rule finding as well as area calculations
Tom Davis' work on proving Pick's theorem for any triangle (and any polygon)
as indicate above, I ask students to indicate the base and perpendicular height that they have used to calculate the areas