153
Question
Find the number of triangles in the given figure:
Find the number of triangles in the given figure:
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Solution
The correct option is A 16
The figure may be labelled as shown.
The simplest triangles are AGE, EGC, GFC, BGF, DGB and ADG i.e. 6 in number.
The triangles composed of two components each are AGC, BGC and ABG i.e. 3 in number.
The triangles composed of three components each are AFC, BEC, BDC, ABF, ABE and DAC i.e. 6 in number.
There is only one triangle i.e. ABC composed of six components.
Thus, there are 6 + 3 + 6 + 1 = 16 triangles in the given figure.
The figure may be labelled as shown.
The simplest triangles are AGE, EGC, GFC, BGF, DGB and ADG i.e. 6 in number.
The triangles composed of two components each are AGC, BGC and ABG i.e. 3 in number.
The triangles composed of three components each are AFC, BEC, BDC, ABF, ABE and DAC i.e. 6 in number.
There is only one triangle i.e. ABC composed of six components.
Thus, there are 6 + 3 + 6 + 1 = 16 triangles in the given figure.
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