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Consider the red barn with all doors locked, and the Norwe-

gian goat, shown below.

The goat is tied at the end of a 30-meter rope. What is the
total grazing area available to the goat (in square meters)?

Consider the red barn with all doors locked, and the Norwe- gian goat, shown below-example-1
User Newgre
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1 Answer

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The total grazing area available to the goat is equal to 1,805.5 square metres

The Norwegian goat can cover an area of a big semicircle with a diameter of 60 m and radius 30m below the red barn, and also a quadrant of a circle with radius 10m to the right of the red barn and another quadrant of a circle with radius 20m to the left side of the red barn.

Area of a circle = πr²

Area of semicircle = πr²/2

Area of a circle quadrant = πr²/4

Using π = 3.14

Area of semicircle below the red barn = [3.14 × (30m)²] ÷ 2 = 2,826 m²/2

Area of semicircle below the red barn = 1,413 m²

Area of a circle quadrant to the right of the red barn = [3.14 × (10m)²] ÷ 4 = 314/4

Area of a circle quadrant to the right of the red barn = 78.5 m²

Area of a circle quadrant to the left of the red barn = [3.14 × (20m)²] ÷ 4 = 1,256/4

Area of a circle quadrant to the left of the red barn = 314 m²

Total grazing area available to the goat is the sum of all three areas calculated above which is: 1,413 m² + 78.5 m² + 314 m² = 1,805.5 m²

User Magomogo
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