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, we have the following dimensions:
- Base = 25 inches
- Height = 15 inches
Now, we can plug in these values into the area formula:
\[ \text{Area} = \frac{1}{2} \times 25 \text{ inches} \times 15 \text{ inches} \]
Calculating that step-by-step:
- First, calculate \( 25 \times 15 \):
\[ 25 \times 15 = 375 \]
- Then multiply by \( \frac{1}{2} \):
\[ \text{Area} = \frac{1}{2} \times 375 = 187.5 \text{ square inches} \]
Now, we know the actual area of the flag is \( 187.5 \) square inches.
Next, we need to find the area of Magnolia’s scale drawing. The base of the scale drawing is given as 10 inches. To find the height of the scaled triangle, we need to determine the scale factor used in the drawing.
The scale factor is calculated by comparing the base lengths of the actual flag and the scale drawing:
\[ \text{Scale factor} = \frac{\text{Base of the scale drawing}}{\text{Base of the actual flag}} = \frac{10 \text{ inches}}{25 \text{ inches}} = \frac{2}{5} \]
Now we apply this scale factor to find the new height of the scale drawing:
\[ \text{New height} = \text{Actual height} \times \text{Scale factor} = 15 \text{ inches} \times \frac{2}{5} = 6 \text{ inches} \]
Now we can find the area of Magnolia’s scale drawing using the base of 10 inches and the new height of 6 inches:
\[ \text{Area of scale drawing} = \frac{1}{2} \times \text{Base} \times \text{Height} = \frac{1}{2} \times 10 \text{ inches} \times 6 \text{ inches} \]
Calculating this step-by-step:
- First, calculate \( 10 \times 6 \):
\[ 10 \times 6 = 60 \]
- Then multiply by \( \frac{1}{2} \):
\[ \text{Area of scale drawing} = \frac{1}{2} \times 60 = 30 \text{ square inches} \]
Thus, the area of Magnolia’s scale drawing of the flag is \(\boxed{30}\) square inches.
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