Question

A sign is being painted that is comprised of 3 small squares with a side length of s and 2 large squares with a side length of x . Write an expression to find the total area of the sign that needs to be painted. (1 point) Responses 3x2−2s2 3 x squared minus 2 s squared 2x2+3s2 2 x squared plus 3 s squared 2x2−3s2 2 x squared minus 3 s squared 3x2+2s2

Answer 1

To find the total area of the sign, we need to consider the areas of both the small squares and the large squares.

1. **Area of one small square**: The area \( A_s \) of one small square is given by:
\[
A_s = s^2
\]
Since there are 3 small squares, the total area of the small squares is:
\[
\text{Total area of small squares} = 3s^2
\]

2. **Area of one large square**: The area \( A_l \) of one large square is given by:
\[
A_l = x^2
\]
Since there are 2 large squares, the total area of the large squares is:
\[
\text{Total area of large squares} = 2x^2
\]

3. **Total area of the sign**: Now we can write an expression for the total area \( A_{\text{total}} \) of the sign:
\[
A_{\text{total}} = \text{Total area of small squares} + \text{Total area of large squares}
\]
\[
A_{\text{total}} = 3s^2 + 2x^2
\]

Therefore, the expression for the total area of the sign that needs to be painted is:
\[
\boxed{2x^2 + 3s^2}
\]