Find the number of triangles in the given figure –
2022
Find the number of triangles in the given figure –
- A.
24
- B.
22
- C.
20
- D.
18
Attempted by 92 students.
Show answer & explanation
Correct answer: B
To count every triangle in a composite figure built from subdivided cells, count in increasing order of size: first the smallest triangles that are not made up of any other counted triangle, then triangles formed by combining two or more adjacent smallest triangles, and finally the largest triangles formed by lines that run across more than one cell. Each distinct triangle — using only lines that are actually drawn as straight, unbroken segments in the figure — must be counted exactly once.
The figure is two square cells stacked one above the other, each cell divided by its two diagonals into four smaller triangles, with an extra triangular “wing” triangle attached to the left side and another to the right side of each cell:
Size | How it is formed | Count |
|---|---|---|
Smallest | 4 quarter-triangles inside each subdivided square (from its two diagonals) plus the 2 wing triangles attached to each square (6 per square) | 12 |
Medium | One full diagonal of a square together with two of its sides (4 per square) | 8 |
Large | One full outer side (left or right), spanning both squares, together with the two diagonals — one from each square — that meet at the shared middle corner | 2 |
12 + 8 + 2 = 22, so the figure contains 22 triangles in total.
Cross-check: each square cell together with its two wing triangles contains 10 triangles on its own (8 inside the subdivided square + 2 wings). The two cells together give 2 × 10 = 20 triangles confined to a single cell. Adding the 2 large triangles that span both cells through the shared middle corner brings the total to 20 + 2 = 22, confirming the count above.