1009.11 – Triangle Count

How many triangles are in this figure?



Count carefully; be systematic! The triangle AEF\triangle AEF has four more like it, BAG,CBH,DCJ, and EDK\triangle BAG,\triangle CBH, \triangle DCJ, \text{ and } \triangle EDK , moving around the large figure clockwise. Similarly the seven additional triangles AFB,AEB,ADH,AKC, and ADC,AFG\triangle AFB, \triangle AEB, \triangle ADH, \triangle AKC, \text{ and } \triangle ADC, \triangle AFG (all containing vertex AA) each has four more around the large figure.

So the total number is 8 ×\times 5 == 40. (Have we counted anything twice? Have we missed any?)