triangles cut into triangles

the main purpose of this work is to provide a focus on triangle areas
particularly with same bases and equal heights (Euclid I. 37)
but there are various optional spin-offs:

• perpendicular lines
• surd lengths
• length and area ratios of similar shapes

 

questions for the triangles above

the team at Puntmat (@puntmat) have found 8 ways (so far) to cut up a 3 by 6 right triangle into three equal areas (i.e. non-congruent thirds):

their post on fractions of geometrical shapes contains many good exercises

many thanks to them











dividing unequally: