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Question

Jenna has a habit of drawing some random shapes whenever she feels bored.
She draws a shape that looks like the one below.
Help Jenna find the number of triangles in the given figure.

A
28
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B
30
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C
12
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D
32
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Solution

The correct option is A 28
Let's first label the figure:
  • Number of simple triangles:
AJG, GJK, GKD, DKH, HKJ, HJB, BJF, FJI, FIC, CIE, EIJ, EJA
= 12
  • Number of triangles formed by joining 2 simple triangles:
JGD, GDH, DHJ, HJG, JFC, FCE, CEJ, EJF
= 8
  • Number of triangles formed by joining 3 simple triangles:
AJD, DJB, BJC, CJA
= 4
  • Number of triangles formed by joining 6 simple triangles:
ADB, DBC, BCA, CAD
= 4

Total number of triangles = 12 + 8 + 4 + 4 = 28

Thus, there are 28 triangles in the given figure.

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