To find the area of Magnolia's scale drawing of the triangular flag, we can start by calculating the area of the original flag and then use the scale to find the area of the drawing.
Step 1: Find the area of the original triangular flag.
The formula for the area \( A \) of a triangle is:
\[ A = \frac{1}{2} \times \text{base} \times \text{height} \]
For the original flag, the base is 25 inches and the height is 15 inches. Plugging in these values:
\[ A = \frac{1}{2} \times 25 \times 15 \]
Now, calculate \( 25 \times 15 \):
\[ 25 \times 15 = 375 \]
Now, find the area:
\[ A = \frac{1}{2} \times 375 = 187.5 \text{ square inches} \]
Step 2: Find the scale factor.
Magnolia's scale drawing has a base length of 10 inches. We find the scale factor by comparing the base lengths:
\[ \text{Scale factor} = \frac{\text{Scale base}}{\text{Original base}} = \frac{10}{25} = \frac{2}{5} \]
Step 3: Find the area of the scale drawing.
The area scales with the square of the scale factor. So, we calculate the area of the scale drawing using the original area and the square of the scale factor:
\[ \text{Scale factor squared} = \left(\frac{2}{5}\right)^2 = \frac{4}{25} \]
Now, multiply the original area by the scale factor squared:
\[ \text{Area of scale drawing} = \text{Original area} \times \text{Scale factor squared} \] \[ \text{Area of scale drawing} = 187.5 \times \frac{4}{25} \]
Now, we calculate \( 187.5 \times \frac{4}{25} \):
- First, find \( 187.5 \div 25 \):
\[ 187.5 \div 25 = 7.5 \]
- Then multiply by 4:
\[ 7.5 \times 4 = 30 \]
Final Answer:
The area of Magnolia’s scale drawing is \( \boxed{30} \) square inches.
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