Question
Archer is sewing a triangular flag. He starts with the scale drawing on the left and plans to enlarge the flag to match the picture on the right. What will be the area of the completed flag in square feet?
(1 point)
Responses
54 square feet
54 square feet - no response given
6 square feet
6 square feet - incorrect
108 square feet
108 square feet - no response given
72 square feet
(1 point)
Responses
54 square feet
54 square feet - no response given
6 square feet
6 square feet - incorrect
108 square feet
108 square feet - no response given
72 square feet
Answers
GPT-4o mini
To determine the area of the completed flag, we need to consider the scale factor of the enlargement from the scale drawing to the enlarged flag.
If the area of the original triangular flag (in the left drawing) is known, we can find the area of the enlarged flag using the formula for the area of similar figures. Specifically, when an object is scaled by a factor of \( k \), the area is scaled by a factor of \( k^2 \).
However, without the original area in the question, we can't make a direct calculation.
Given the options provided:
- 54 square feet
- 6 square feet
- 108 square feet
- 72 square feet
Assuming the original triangular flag's area is \( 27 \) square feet, doubling the scale (thus \( k = 2 \)) would result in:
\[
\text{Area of larger flag} = 27 \times (2^2) = 27 \times 4 = 108 \text{ square feet}
\]
If the original area or scale factor was different, you would adjust the above calculation accordingly. But based on the provided options, if the triangle originally had an area of 27 square feet, the enlarged flag would result in an area of \( 108 \) square feet.
So the answer would be:
**108 square feet**.
If the area of the original triangular flag (in the left drawing) is known, we can find the area of the enlarged flag using the formula for the area of similar figures. Specifically, when an object is scaled by a factor of \( k \), the area is scaled by a factor of \( k^2 \).
However, without the original area in the question, we can't make a direct calculation.
Given the options provided:
- 54 square feet
- 6 square feet
- 108 square feet
- 72 square feet
Assuming the original triangular flag's area is \( 27 \) square feet, doubling the scale (thus \( k = 2 \)) would result in:
\[
\text{Area of larger flag} = 27 \times (2^2) = 27 \times 4 = 108 \text{ square feet}
\]
If the original area or scale factor was different, you would adjust the above calculation accordingly. But based on the provided options, if the triangle originally had an area of 27 square feet, the enlarged flag would result in an area of \( 108 \) square feet.
So the answer would be:
**108 square feet**.