question_answer

How many quadrilaterals are there in the figure given below?

A) 64

B) 60    

C) 58

D) 56

Correct Answer: B

Solution :

Explanation: The main four sided figure is ABCD i.e. - 1 quadrilateral The simplest four sided figures are: AIEL, IJLM, ELGP, LMPQ, MNQR, NORS, OFSH, RSUV and SHVD i.e. - 9 quadrilaterals. The quadrilaterals divided into two parts are: AJEM, AIGP, IJPQ, EMGQ, LNPR, JKMN, KBNF, MOQS, NFRH, NOUV, OFVD, GQCT, QRTU and RHUD i.e. ? 14 quadrilaterals. The quadrilaterals divided into three parts are. IKLN, ENGR, LOPS, MFQH, JKQR, JNQU, MNTU and QSTV i.e. - 9 quadrilaterals. The quadrilaterals divided into four parts are: AKEN, JBMF, EOGS, LFPH, GRCU, QHTD, AJGQ, EMCT, KBRH and NFUD i.e. ? 10 quadrilaterals. The quadrilaterals divided into five part are: IBLF, EFGH, GSCV and JKTU i.e. - 4 quadrilaterals. The quadrilaterals divided into six parts are: ABEF, GHCD, AJCT, and KBUD i.e. ? 4 quadrilaterals. The quadrilaterals Divided into seven parts are: AKGR, JBQH, ENCU and MFTD i.e. - 4 quadrilaterals. Other quadrilaterals are IBPH, EOCV, ABGH, EFCD, AKCU and JBTD i.e. - 6 quadrilaterals. So, the total number of quadrilaterals is: \[1+9+14+8+10+4+4+4+6=60\]