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Question
Tony wants to find the number of triangles in a shape drawn on the board. Help him find the total number of triangles.
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Solution
Let's label the figure.
The simple triangles are IEF, IED, AGF, AGB, BGE, EFG, BHE, BHC, CHD, and DEH. There are 10 simple triangles in the figure.
The triangles composed of two components each are IFD, AFE, ABE, BAF, BEF, EBC, CDE, BDE, and BCD. There are 9 such traingles.
The triangles composed of three components each are IFB and IDB. There are 2 such triangles.
The triangles composed of three components each are FDB and ACE. There are 2 such traingles.
Total number of triangles in the given figure = 10 + 9 + 2 + 2 = 23
The simple triangles are IEF, IED, AGF, AGB, BGE, EFG, BHE, BHC, CHD, and DEH. There are 10 simple triangles in the figure.The triangles composed of two components each are IFD, AFE, ABE, BAF, BEF, EBC, CDE, BDE, and BCD. There are 9 such traingles.
The triangles composed of three components each are IFB and IDB. There are 2 such triangles.
The triangles composed of three components each are FDB and ACE. There are 2 such traingles.
Total number of triangles in the given figure = 10 + 9 + 2 + 2 = 23
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