A big triangle made up of many smaller triangles
How am I supposed to count the total amount of triangles in this figure?
2026-03-28 14:53:29.1774709609
Counting triangles in a big triangle
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There are 2 cases. First case, where the large triangle is cut into 3 smaller triangles all touching at the middle. Each of these small triangles consist of 4 triangles. Then there would be 10 triangles in each small triangle. Since there are 3 small triangles, 3 x 10 = 30 triangles.
Case 2, whereby each line cuts the large triangle into 2 triangles. There are 6 of these lines, so 6 x 2 = 12 triangles.
Total number of triangles would be 12 + 30 + 1(we mustn't forget the big triangle) = 43 triangles in total.