Question

find the area of Field KLMNOP which
is hexagonal shape given that
LO -55m, MN = 28m, KM= 48m,
KQ - 20 m, PR=16m,
LR = 45m
and QO=40m.​

Answer 1

Given : field KLMNOP   in hexagonal shape

LO = 55 m, MN = 28 m, KM = 48 m, KQ = 20 m, PR = 16 m,  LR = 45 m and QO = 40m.​

To Find : area of field KLMNOP

Solution:

LO = 55  m

LR = 45  m

=> RO = 55 - 45 = 10  m

QR = QO - RO

=> QR = 40 - 10

=> QR = 30 m

LQ = LR - QR =  45 - 30 = 15  m

MQ = KM - KQ

=> MQ = 48 - 20

=> MQ = 28  m

area of field KLMNOP

= Area of ΔKQL  + area of trapezium KQRP + Area of Δ PRO + area of trapezium LOMN

Area of ΔKQL  = (1/2) KQ * LQ

= (1/2) 20 * 15

= 150 m²

area of trapezium KQRP  = (1/2) ( KQ + PR) * QR

=  (1/2)(20 + 16) * 30

= 540  m²

Area of Δ PRO = (1/2) * PR * RO

= (1/2) * 16 * 10

= 80  m²

area of trapezium LOMN = (1/2)(LO + MN) * MQ

= (1/2) (55 + 28) 28

= 1162   m²

Total area of field =  150 + 540 + 80 + 1162  =  1932  m²

area of field KLMNOP = 1932  m²

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