To find the area of the triangular flag, we can use the formula for the area of a triangle:
\[ \text{Area} = \frac{1}{2} \times \text{base} \times \text{height} \]
For the actual flag, the base is 25 inches and the height is 15 inches. Let's calculate the area:
\[ \text{Area}_{\text{actual}} = \frac{1}{2} \times 25 \times 15 \]
Calculating this step by step:
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Calculate \(25 \times 15\): \[ 25 \times 15 = 375 \]
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Now, compute \(\frac{1}{2} \times 375\): \[ \frac{1}{2} \times 375 = 187.5 \]
Thus, the area of the actual triangular flag is \(187.5\) square inches.
Now, we need to find the area of Magnolia's scale drawing, where the base is scaled down to 10 inches. Since we need to keep the same proportions of the triangle, we need to find the scale factor.
The scale factor from the actual triangle's base to the scale drawing's base is:
\[ \text{Scale factor} = \frac{\text{base of scale drawing}}{\text{base of actual flag}} = \frac{10}{25} = \frac{2}{5} \]
The height of the scale drawing can be calculated using the same scale factor:
\[ \text{Height of scale drawing} = \text{actual height} \times \text{scale factor} = 15 \times \frac{2}{5} = 6 \]
Now we can find the area of the scale drawing:
\[ \text{Area}{\text{scale}} = \frac{1}{2} \times \text{base} \times \text{height} \] Substituting in the values for the scale drawing: \[ \text{Area}{\text{scale}} = \frac{1}{2} \times 10 \times 6 \]
Calculating this:
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Calculate \(10 \times 6\): \[ 10 \times 6 = 60 \]
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Now, compute \(\frac{1}{2} \times 60\): \[ \frac{1}{2} \times 60 = 30 \]
Thus, the area of Magnolia's scale drawing is \(\boxed{30}\) square inches.