To find the area of Magnolia's scale drawing of the triangular flag, we can follow these steps:
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Find the area of the actual flag.
- The formula for the area of a triangle is:
\[ \text{Area} = \frac{1}{2} \times \text{base} \times \text{height} \] - The actual height of the flag is 15 inches, and the base length is 25 inches.
- So, we plug those numbers into the formula: \[ \text{Area} = \frac{1}{2} \times 25 \times 15 \]
- The formula for the area of a triangle is:
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Do the multiplication:
- First, calculate \( 25 \times 15 \): \[ 25 \times 15 = 375 \]
- Now, divide by 2: \[ \frac{375}{2} = 187.5 \]
- So, the area of the actual flag is 187.5 square inches.
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Find the scale factor.
- The base of the actual flag is 25 inches, and in Magnolia's scale drawing, the base is 10 inches.
- To find the scale factor, we divide the base of the scale drawing by the base of the actual flag: \[ \text{Scale factor} = \frac{10}{25} = \frac{2}{5} \]
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Apply the scale factor to find the height of the scale drawing.
- Since the height also scales down by the same factor, we multiply the actual height by the scale factor: \[ \text{Height of scale drawing} = 15 \times \frac{2}{5} = 6 \]
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Find the area of the scale drawing using the new dimensions.
- Now we know the base of the scale drawing is 10 inches and the height is 6 inches. So we use the area formula again: \[ \text{Area of scale drawing} = \frac{1}{2} \times 10 \times 6 \]
- Do the calculation: \[ 10 \times 6 = 60 \] \[ \frac{60}{2} = 30 \]
- So, the area of Magnolia's scale drawing is 30 square inches.
In conclusion, the area of Magnolia’s scale drawing of the flag is 30 square inches.