Question
a sign is being painted that is calm comprised of three small squares with a side length of S and two large squares with a side length of X write an expression to find the total area of the sign that needs to be painted
Answers
GPT-4o mini
To find the total area of the sign that needs to be painted, we will calculate the area of both the small squares and the large squares and then sum them up.
1. **Area of the small squares**:
- Each small square has a side length of \( S \).
- The area of one small square is \( S^2 \).
- Since there are three small squares, their total area is:
\[
3 \times S^2 = 3S^2
\]
2. **Area of the large squares**:
- Each large square has a side length of \( X \).
- The area of one large square is \( X^2 \).
- Since there are two large squares, their total area is:
\[
2 \times X^2 = 2X^2
\]
3. **Total area of the sign**:
- Now, we combine the areas of the small and large squares:
\[
\text{Total Area} = \text{Area of small squares} + \text{Area of large squares} = 3S^2 + 2X^2
\]
Thus, the expression for the total area of the sign that needs to be painted is:
\[
3S^2 + 2X^2
\]
1. **Area of the small squares**:
- Each small square has a side length of \( S \).
- The area of one small square is \( S^2 \).
- Since there are three small squares, their total area is:
\[
3 \times S^2 = 3S^2
\]
2. **Area of the large squares**:
- Each large square has a side length of \( X \).
- The area of one large square is \( X^2 \).
- Since there are two large squares, their total area is:
\[
2 \times X^2 = 2X^2
\]
3. **Total area of the sign**:
- Now, we combine the areas of the small and large squares:
\[
\text{Total Area} = \text{Area of small squares} + \text{Area of large squares} = 3S^2 + 2X^2
\]
Thus, the expression for the total area of the sign that needs to be painted is:
\[
3S^2 + 2X^2
\]