(1) 132.67 square meters
(2) 379.94 square meters
Step-by-step explanation:
A barn is in the shape of a rectangle with each corner angle a right angle.
[tex] \therefore Central\: \angle \:(\theta) =90°[/tex]
Since, goat is tied at a corner of the barn, so she would be able to graze the grass of sector of circle with radius (r) = 13 m.
Area of field grazed by goat = area of sector of circle
[tex] = \frac{ \theta}{360 \degree} \times \pi {r}^{2} \\ \\ = \frac{90 \degree}{360 \degree} \times 3.14 \times {13}^{2} \\ \\ = \frac{1}{4} \times 3.14 \times 169\\ \\ = \frac{1}{4} \times530.66 \\ = 132.665 \\ = 132.67 \: {m}^{2} [/tex]
[tex] (2) \\ similarly \: for \: r \: = 22 \: m \\ area \: of \: sector = 379.94 \: {m}^{2} [/tex]
