Question

How many triangles are there in the given figure?

[a] 10
[b] 11
[c] 13
[d] 15

Answer 1

Hint:Start listing all the possible triangles in order, i.e. from virtually the smallest area to the largest area. Count the total number of triangles listed. Hence find the number of triangles in the diagram.

Complete step-by-step answer:
We will start listing the triangles in ascending order of their area. Also we need to make sure that no triangle is repeated. Hence we will write the name of the triangle in alphabetic order of its vertices.

We have the following triangles
[i] AEH [ii] ADH [iii] CDI [iv] CFI [v] BFK [vi] BEK [vii] EFI [viii] DEI [ix] AED [x] BEF [xi] CDF [xii] DEF [xiii] CDE [xiv] CFE [xv] ABC.
Hence, we have listed all the triangles in the above diagram,
Hence, there are 15 triangles in the above diagram
Hence option [d] is correct.

Note: In these types of questions students usually count a number of triangles more than once or forget to count a triangle. This can be avoided by following a sequential way of listing the triangles and making sure that no triangle is counted more than once, like in the above question, we wrote the triangles in sequential order of their area and also to minimize the risk of overcounting, we wrote their names in alphabetical order of their letters.