To find the area of Magnolia's scale drawing of the triangular flag, we can first calculate the area of the actual flag and then find the area of the scaled-down version.
Step 1: Calculate the area of the actual flag.
The area \(A\) of a triangle can be calculated using the formula:
\[ A = \frac{1}{2} \times \text{base} \times \text{height} \]
In this case, the base of the actual flag is 25 inches and the height is 15 inches.
Substituting in the values:
\[ A = \frac{1}{2} \times 25 \times 15 \]
Step 2: Perform the multiplication.
Calculate \(25 \times 15\):
\[ 25 \times 15 = 375 \]
Now substitute that value back into the area formula:
\[ A = \frac{1}{2} \times 375 = \frac{375}{2} = 187.5 \]
So, the area of the actual flag is 187.5 square inches.
Step 3: Find the scale factor.
Magnolia's scale drawing has a base length of 10 inches. To find the scale factor, we compare the base lengths:
\[ \text{Scale factor} = \frac{\text{base of scale drawing}}{\text{base of actual flag}} = \frac{10}{25} = \frac{2}{5} \]
Step 4: Calculate the area of the scale drawing.
Since the area scales with the square of the scale factor, we need to square the scale factor:
\[ \text{Scale factor for area} = \left(\frac{2}{5}\right)^2 = \frac{4}{25} \]
Now, we can find the area of the scale drawing:
\[ \text{Area of scale drawing} = \text{Area of actual flag} \times \frac{4}{25} \]
Substituting the area of the actual flag:
\[ \text{Area of scale drawing} = 187.5 \times \frac{4}{25} \]
Step 5: Perform the multiplication for the area of the scale drawing.
Calculating \(187.5 \times \frac{4}{25}\):
To simplify, first find the value of \(187.5 \div 25\):
\[ 187.5 \div 25 = 7.5 \]
Now multiply this by 4:
\[ 7.5 \times 4 = 30 \]
Therefore, the area of Magnolia’s scale drawing is 30 square inches.
\[ \text{Final answer: } 30 \text{ square inches} \]
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