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How many triangles are in the given shape?
Question

How many triangles are in the given shape?

A.

15

B.

30

C.

18

D.

16

Correct option is D

  1. Small triangles (basic divisions):

    • The figure is divided into 8 small triangles by the intersecting lines within the square.
  2. Triangles formed by combining two small triangles:

    • In each quadrant (top-left, top-right, bottom-left, bottom-right), we can combine two small triangles to form a larger triangle. Since there are 4 quadrants:
      • 4 larger triangles.
  3. Triangles formed by combining four small triangles:

    • The triangles formed by combining all four triangles within one-half of the square (top or bottom, left or right):
      • 2 triangles (one for the top half and one for the bottom half).
  4. Triangles formed by combining all eight triangles (the entire square):

    • The largest triangles are formed by combining all eight triangles:
      • 2 triangles (one pointing up and one pointing down).

Total count:

  • Small triangles = 8
  • Larger triangles (combining 2 small ones) = 4
  • Larger triangles (combining 4 small ones) = 2
  • Largest triangles (combining all 8 small ones) = 2

Total triangles = 8 + 4 + 2 + 2 = 16

Final Answer: 

16 triangles

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