SOLUTION: A farmer has fenced off his housing area, which is shown in the diagram below. There is a post at each of the points A and F, to which the farmer sometimes attaches a 30m rope that

Algebra ->  Surface-area -> SOLUTION: A farmer has fenced off his housing area, which is shown in the diagram below. There is a post at each of the points A and F, to which the farmer sometimes attaches a 30m rope that      Log On


   

Question 1149602: A farmer has fenced off his housing area, which is shown in the diagram below. There is a post at each of the points A and F, to which the farmer sometimes attaches a 30m rope that is tied to his donkey. This provides the donkey with either one of two grazing areas outside the housing area. Find the difference in the areas available for grazing, in m2.
Diagram: https://imgur.com/a/xRRw3rz
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Attached at point F, Add up quarter circles:
(1) +%281%2F4%29%2Api%2A30%5E2+
(2) +%281%2F4%29%2Api%2A30%5E2+
(3) +%281%2F4%29%2Api%2A4%5E2+
(4) +%281%2F4%29%2Api%2A30%5E2+
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+%283%2F4%29%2Api%2A30%5E2+%2B+%281%2F4%29%2Api%2A4%5E2+
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Attached at point A, Add up quarter circles:
(1) +%281%2F4%29%2Api%2A30%5E2+
(2) +%281%2F4%29%2Api%2A4%5E2+
(3) +%281%2F4%29%2Api%2A30%5E2+
(4) +%281%2F8%29%2Api%2A30%5E2+ ( 1/8 of a circle )
(5) +%281%2F8%29%2Api%2A12%5E2+ ( 1/8 of a circle )
(6) +%281%2F2%29%2A%28+9%2Asqrt%282%29+%29%5E2+=+81+ ( triangle that donkey can graze in )
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The difference of these results is:
+%281%2F8%29%2Api%2A30%5E2+%2B++%281%2F8%29%2Api%2A12%5E2+%2B+81+
+%281%2F8%29%2Api%2A%28+30%5E2+%2B+12%5E2+%29+%2B+81+
The attachment a point A traces out the largest area
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