first, we have 3/4ths of a full circle with radious 12, the length of the rope. So 12 squared is 144 * 3/4ths which is 108pie. Then the horse wraps around one side of the barn with radius 2 (12-10), and forms 1/4 of a circle/ So 2 squared is 4 * 1/4 is 1. Now we have a total of 109 pie sq. meters. Then, the horse wraps around the other side of the barn, and forms another 1/4th circle with radius 4 (12-8). Thus, 4 squared is 16 * 1/4th equals 4. So we add 4 to 109,which gives us 113 pie sq. meters.