Question

A goat is tethered by a 6 metre rope to the outside corner of a shed measuring 4 metres by 5 metres in a grassy field. What area of grass can the goat graze?

Answer 1

Since the corner of the shed is a 90 degree angle. That leaves 3/4 of a circle with radius of 6.
\[(3/4)*\pi*6^{2} = 27 \pi\]
Also , the goat can reach around the corners by 2 on the short sides and 1 on long side.
creating 2 90 degree sectors of additional grazing area.
\[(1/4)*\pi*2^{2} = \pi\]
\[(1/4)*\pi*1^{2} = \pi/4\]
\[27 \pi + \pi + \pi/4 = 28.25 \pi\]

Answer 2

Correct!