How many triangles are there in the given figure?

2016

How many triangles are there in the given figure?

image.png

  1. A.

    23 or more

  2. B.

    20

  3. C.

    16

  4. D.

    12

Attempted by 5 students.

Show answer & explanation

Correct answer: A

1. Count the smallest, individual triangular regions first: There are 5 in the top rectangular section, 5 in the middle section, and 2 in the bottom pointed tip, giving 12 basic triangles. 2. Next, look for triangles formed by combining 2 or more smaller regions. The entire bottom tip forms 1 large triangle. 3. Trace the longer continuous straight lines to find large overlapping triangles. For example, the diagonals create 4 large triangles spanning across the middle horizontal line, and 4 large right-angled triangles in the outer corners of the rectangular portion. 4. Adding the 12 base triangles to the numerous larger combined geometric shapes (12 + 1 + 4 + 4 + ...) quickly pushes the total count to 23 or more. Final Answer: Option A

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