How many triangles #4

Answer with Solution

Looking at the symmetry, we can divide this triangle in 5 equal parts(square) and we will first count the number of triangles in each part and then number of triangles formed by combining 2 or more parts together.
Number of triangles in one square: 8(non overlapping triangles) + 8(overlapping triangles with middle lines a part of the triangle) =16*5 = 80
Number of triangles by taking two squares(one middle and one other) at a time: 4*4(there are four such combinations) = 16
Number of triangles by taking (only) three squares(one middle and two others) at a time: 4(all squares should be a part of the triangle) *4(four such combinations) = 16
Number of triangles by taking 4 squares together: 2 *4(four such combinations) = 8

Thus total number of triangles = 80 + 16 + 16 + 8 = 120.