The fenced flower bed has the shape of a regular hexagon. The tops are formed by fence posts. The fence around the flowerbed measures 60 m. A goat is tied to one of the pillars from the outside and grazes on the surrounding meadow (the goat should not enter the flowerbed). The twine measures 24 m. How many square meters of the meadow can a goat graze?

Correct answer:

S =  1428.3775 m2

Step-by-step explanation:

o=60 m r=24 m  a=o/6=60/6=10 m  r>a  α=3602 60=240  S1=π r2 α360=3.1416 242 2403601206.3716 m2  β=60  S2=π (ra)2 β360=3.1416 (2410)2 60360102.6254 m2  S3=π (r2 a)2 β360=3.1416 (242 10)2 603608.3776 m2  S=S1+2 S2+2 S3=1206.3716+2 102.6254+2 8.37761428.3775=1428.3775 m2   Verifying Solution:   M=π r2=3.1416 2421809.5574 m2  M>S

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