1.

Find the number of straight lines and the number of triangles in the complex figure given below .

Answer»


Solution :Usually VERTICES are not marked, but we can mark to MAKE the counting easy.
Number of straight lines are :
AB,BC, CD, DA, AC, BD, EH, AH, DH
So there are 9 straight lines in the diagram . Now count triangles :
Number of small triangles are (containing one component)
AGH, GHD, AFD, DGF, FBE and FCE = 6
Number of triangles with two components:
AHF, DHF, AHD, AFD, AFB, DFC , FBC = 7
Number of triangles with four components:
ABC, ADC, CDB adn ADB = 4
`therefore` TOTAL number of triangle CONTAINED in the figure= 6+7+4 =17


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