To find the area of the field represented by the diagram, we first need to convert the dimensions of the diagram from inches to yards using the scale provided (1 inch represents 20 yards).
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Convert the dimensions from inches to yards:
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Length: \(5 \frac{1}{2}\) inches
- Convert \(5 \frac{1}{2}\) to an improper fraction: \[ 5 \frac{1}{2} = \frac{11}{2} \text{ inches} \]
- Now convert to yards: \[ \text{Length in yards} = \frac{11}{2} , \text{inches} \times 20 , \text{yards/inch} = \frac{11 \times 20}{2} = \frac{220}{2} = 110 , \text{yards} \]
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Width: \(3\) inches
- Convert to yards: \[ \text{Width in yards} = 3 , \text{inches} \times 20 , \text{yards/inch} = 60 , \text{yards} \]
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Calculate the area of the field:
- Area \(A\) is given by the formula \(A = \text{Length} \times \text{Width}\): \[ A = 110 , \text{yards} \times 60 , \text{yards} = 6600 , \text{square yards} \]
Thus, the area of the field is \(6600\) square yards.