Answer:
239
Step-by-step explanation:
The area the goat can graze is a circular segment (a circle cut by a chord), where the radius is 10 m and the distance from the center to the chord is 6 m. Here's a graph: desmos.com/calculator/qmstllv4dx
To find the area, we can split this into two shapes: a sector and an isosceles triangle. desmos.com/calculator/hvsor3mqps
To find the areas, we first must find the vertex angle of the triangle. We can do that using cosine:
cos(θ/2) = 6/10
θ/2 = 53.13°
θ = 106.26°
The area of the triangle can be found with the SAS formula:
A = ½ ab sin C
A = ½ (6) (6) (sin 106.26°)
A = 17.28
The area of the sector is:
A = πr² (θ / 360°)
A = π (10)² ((360° − 106.26°) / 360°)
A = 221.43
The total area is 17.28 + 221.43 = 238.71. Rounded to the nearest square meter, the goat can graze an area of 239 m².
