To find the area of Magnolia’s scale drawing of the triangular flag, we start by calculating the area of the actual flag, and then determine the area of the scale drawing based on the change in size.
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Calculate the area of the actual flag: The area \(A\) of a triangle can be calculated using the formula: \[ A = \frac{1}{2} \times \text{base} \times \text{height} \] For the actual flag:
- Height = 15 inches
- Base = 25 inches
Plug in the values: \[ A = \frac{1}{2} \times 25 \times 15 \] \[ A = \frac{1}{2} \times 375 = 187.5 \text{ square inches} \]
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Determine the scale factor: The base of the actual flag is 25 inches and the base of the scale drawing is 10 inches. The scale factor \(S\) is: \[ S = \frac{\text{base of scale drawing}}{\text{base of actual flag}} = \frac{10}{25} = \frac{2}{5} \]
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Scaling down the area: When an object is scaled down, the area is affected by the square of the scale factor. Therefore, the area of the scale drawing \(A_{scale}\) can be calculated using: \[ A_{scale} = A \times S^2 \] Where \(S^2\) is: \[ S^2 = \left(\frac{2}{5}\right)^2 = \frac{4}{25} \]
Now calculate the area of the scale drawing: \[ A_{scale} = 187.5 \times \frac{4}{25} \] \[ A_{scale} = 187.5 \times 0.16 = 30 \]
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Final answer: Therefore, the area of Magnolia’s scale drawing is: \[ \text{Area of Magnolia's scale drawing} = 30 \text{ square inches} \]
So, the answer is 30 square inches.
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