Question

Find the area of polygon MNOPQR if MP = 9 cm, MD = 7 cm, MC = 6 cm, MB = 4 cm, MA = 2 cm. 

NA, OD, QC and RB are perpendiculars to diagonal MP.

Answer 1

Area of MNOPQR

 = ar △MAN + ar  ADON + ar △DOP + ar △CQP + ar BCQR + ar △MBR 

Hence CP = MP – MC = 9 – 6 = 3 cm 

BC = MC – MB = 6 – 4 = 2 cm 

AB = MB – MA = 4 – 2 = 2 cm

DP = MP – MD = 9 – 7 = 2 cm

AD = MD – MA = 7 – 2 = 5 cm

∴ Area of MNOPQR

= 2.5 + (2.5 × 5.5) + 3 + 3 + 4.5 + (2 × 2.5) 

= 2.5 + 13.75 + 3 + 3 + 4.5 + 5 

= 31.75 sq. cms.