Question

A goat is grazing outside of a rectangular barn that has dimensions 20 ft by 30 ft.

He's tied to a corner of the barn with a 12 ft rope. Find the grazing area of the goat.

Answer 1

Tied to the corner

Means 1part among 4parts of circle or a quarter area

So grazing field

• πr²-1/4πr²
• 3/4πr²
• 3/4(12)²π
• 3/4(144)π
• 108π
• 339.3ft²

Answer 2

• 108π ft² or 339.29 ft²

Explanation:

Refer to attached picture.

The grazing area of the goat is 3/4 of area of circle with 12 ft radius:

• A = 3/4(πr²) = 3/4(π*12²) = 108π or 339.29 ft²