To find the area of Magnolia's scale drawing, we first calculate the area of the actual triangular flag and then use that to find the area of the scale drawing.
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Calculate the area of the actual triangular flag:
The formula for the area \( A \) of a triangle is given by:
\[ A = \frac{1}{2} \times \text{base} \times \text{height} \]
For the actual flag, the base is 25 inches and the height is 15 inches:
\[ A_{\text{actual}} = \frac{1}{2} \times 25 \text{ in} \times 15 \text{ in} = \frac{1}{2} \times 375 \text{ in}^2 = 187.5 \text{ in}^2 \]
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Determine the scale factor:
The base length of Magnolia's scale drawing is 10 inches, while the actual base length is 25 inches. The scale factor \( k \) can be found as follows:
\[ k = \frac{\text{scale base}}{\text{actual base}} = \frac{10 \text{ in}}{25 \text{ in}} = \frac{2}{5} \]
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Calculate the area of the scale drawing:
The area scales with the square of the scale factor. Therefore, the area of the scale drawing \( A_{\text{scale}} \) can be calculated as:
\[ A_{\text{scale}} = A_{\text{actual}} \times k^2 = 187.5 \text{ in}^2 \times \left(\frac{2}{5}\right)^2 \] \[ k^2 = \left(\frac{2}{5}\right)^2 = \frac{4}{25} \]
Then,
\[ A_{\text{scale}} = 187.5 \text{ in}^2 \times \frac{4}{25} \] \[ = 187.5 \times 0.16 = 30 \text{ in}^2 \]
Thus, the area of Magnolia's scale drawing is \( \boxed{30} \text{ in}^2 \).