question_answer

Count the number of parallelograms in the figure given below

A) 35

B) 36

C) 37

D) 38

Correct Answer: B

Solution :

Explanation: The main parallelograms are AFGK and GKMR i.e. - 2 parallelograms the simplest parallelograms are BCHI, DEJL, EFLK, HINO, JLPQ and LKQR i.e. - 6 parallelograms. The parallelograms divided into two parts are: ABGH, CDIJ, DFJK, GHMN, IJOP, JKPR, GBNH and IDPJ i.e. - 8. The parallelograms divided into three parts are: ACGI, BDGI, BDHJ, CEIL, GIMO, GINP, HJNP and ILOQ i.e. - 8 parallelograms. The parallelograms divided into four parts are. BEHL, CFIK, HLNQ and IKOR i.e. - 4 parallelograms. The parallelogram divide into five parts are: ADGJ, BFHK, GJMP HKNR i.e. ? 4 Parallelograms. Other parallelograms are: AEGL, GLMQ, ACNP and BDMO i.e. - 4 parallelograms So, the total number of parallelograms are: \[2+6+8+8+4+4+4=36\]