In this paragraph, the important calculation points are:
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The area of the actual flag is first calculated using the formula for the area of a triangle: \( A = \frac{1}{2} \times \text{base} \times \text{height} \).
- Given values: Height = 15 inches, Base = 25 inches.
- The area calculated is \( A = \frac{1}{2} \times 25 \times 15 = 187.5 \) square inches.
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The scale factor for the drawing is determined by comparing the base lengths of the actual flag and the scale drawing.
- Scale drawing's base = 10 inches, Actual base = 25 inches.
- The scale factor is \( \frac{10}{25} = \frac{2}{5} \).
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The area scales with the square of the scale factor, so we square \( \frac{2}{5} \):
- \( \left( \frac{2}{5} \right)^2 = \frac{4}{25} \).
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Finally, the area of the scale drawing is calculated by multiplying the actual area by the squared scale factor:
- \( \text{Area of drawing} = 187.5 \times \frac{4}{25} = 30 \) square inches.
Thus, the conclusion is that the area of Magnolia's scale drawing is 30 square inches.