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A goat (point ) is tied with a 6-foot rope to the corner of a shed. The floor of the shed is a square whose sides are each 3 feet long. The shed is closed and the goat can't go inside. The space all around the shed is flat, grassy, and the goat can't reach any other structures or objects. What is the area over which the goat can roam?

Respuesta :

sqdancefan
The area available to the goat is 3/4 of a circle with 6 ft radius plus 2/4 of a circle with 3 ft radius.

A = (3/4)π*(6 ft)² + (1/2)π*(3 ft)²
  = π*((3/4)*36 +(1/2)*9) ft²
  = 31.5π ft² ≈ 98.96 ft²

The goat can roam over an area of about 99 ft².

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