To find the area of Magnolia's scale drawing of the triangular flag, we first need to use the area formula for a triangle, which is:
\[ \text{Area} = \frac{1}{2} \times \text{base} \times \text{height} \]
Step 1: Calculate the area of the actual flag
The actual flag has a height of 15 inches and a base length of 25 inches. Plugging 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, multiply the base and the height: \[ 25 \times 15 = 375 , \text{square inches} \]
-
Now, multiply by \(\frac{1}{2}\): \[ \frac{1}{2} \times 375 = 187.5 , \text{square inches} \]
So, the area of the actual flag is 187.5 square inches.
Step 2: Calculate the area of Magnolia's scale drawing
Magnolia's scale drawing has a base of 10 inches. To find the height of the scale drawing, we need to maintain the same ratio as the actual flag.
The ratio of the base lengths is: \[ \text{Scale ratio} = \frac{\text{Base of scale drawing}}{\text{Base of actual flag}} = \frac{10}{25} = \frac{2}{5} \]
Since both height and base are proportional, the height of the scale drawing will also follow this ratio.
Calculating the height of the scale drawing: \[ \text{Height of scale drawing} = \text{Height of actual flag} \times \text{Scale ratio} = 15 \times \frac{2}{5} = 6 , \text{inches} \]
Step 3: Calculate the area of the scale drawing
Now we use the height of the scale drawing (6 inches) and the base length (10 inches) in the area formula:
\[ \text{Area} = \frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times 10 , \text{inches} \times 6 , \text{inches} \]
-
Multiply the base and the height: \[ 10 \times 6 = 60 , \text{square inches} \]
-
Now, multiply by \(\frac{1}{2}\): \[ \frac{1}{2} \times 60 = 30 , \text{square inches} \]
Conclusion
The area of Magnolia’s scale drawing is 30 square inches.