Find the area of field KLMNOP Fig. (iv) which is in hexagonal shape, given that LO = 55 m, MN = 28 m,KM = 48 m, KQ = 20 m,PR = 16 m, LR = 45 m and QO = 40m.
Answers
Answer:
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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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