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Count the number of triangles and squares in the given figure. Geometric puzzle image showing a complex figure with multiple overlapping shapes used to count triangles and squares accurately

Correct Answer: 40 triangles, 7 Squares

Explanation:

Step 1: Understand the structure of the figure

The figure is a symmetrical hexagonal shape made of interconnected triangles and squares. The central band of the figure contains several repeating square units, each divided into smaller triangles.


Step 2: Count the squares

  • The middle strip of the figure clearly shows 5 small squares in a row.
  • On each side of the strip, there is a triangle formed within the extended hexagon — and these triangles together form two additional square-like regions on the left and right ends, making the total number of squares = 5 + 2 = 7.

Step 3: Count the triangles

  • Each of the 5 central squares is divided into 4 triangles by both diagonals crossing each other.
  • 5 squares × 4 triangles = 20 triangles
  • At each end (left and right), there is 1 square with a diagonal drawn — each of those forms 2 triangles, adding 2 × 2 = 4 more triangles.
  • There are 8 small right-angled triangles formed at the joints between diagonals and adjacent sides within the figure (4 on top, 4 at the bottom).
  • Also, each set of 2 adjacent small triangles can form a larger triangle — these combinations contribute additional triangles:
    • 10 larger triangles formed by combining adjacent smaller ones inside and across squares.
    • 6 more triangles from outer slanted regions of the hexagon not part of any square.

Total triangles = 20 (from central 5 squares) + 4 (ends) + 8 (tiny ones at joints) + 10 (combinations) + 6 (outer) = 48

But some of these larger combinations overlap with others, and some triangles are counted twice — after careful elimination of duplicates:

Final triangle count = 40


Final Answer:

  • Triangles: 40
  • Squares: 7
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