To find the area of the triangular flag and then calculate the area of Magnolia's scale drawing, we can follow these steps:
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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 length is 25 inches and the height is 15 inches. Plugging in these values: \[ A = \frac{1}{2} \times 25 \times 15 \]
Calculating that: \[ A = \frac{1}{2} \times 375 = 187.5 \text{ square inches} \]
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Find the scale factor for Magnolia's drawing:
The original base is 25 inches, and the scale drawing has a base of 10 inches. To find the scale factor, divide the lengths: \[ \text{Scale factor} = \frac{10}{25} = \frac{2}{5} \]
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Use the scale factor to find the height of Magnolia's drawing:
Since both the base and height of the triangle will be scaled down by the same factor, we can find the new height: \[ \text{Height of scale drawing} = 15 \times \frac{2}{5} = 6 \text{ inches} \]
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Calculate the area of Magnolia's scale drawing:
Plug the scaled dimensions into the area formula: \[ A_{\text{scale}} = \frac{1}{2} \times \text{base (scale)} \times \text{height (scale)} \] \[ A_{\text{scale}} = \frac{1}{2} \times 10 \times 6 \]
Calculating that: \[ A_{\text{scale}} = \frac{1}{2} \times 60 = 30 \text{ square inches} \]
So, the area of Magnolia’s scale drawing is \( \boxed{30} \) square inches.