A sign is being painted that includes 3 small squares with a side length of s and 2 large ones with a side length of S. Write an expression to find the total area of the sign that needs to be painted.(1 point)
A) 2S^2+3s^2
B) 3S^2+2s^2
C) 2S^2−3s^2
D) 3S^2−2s^2
B) 3S^2+2s^2
To find the total area of the sign that needs to be painted, we need to calculate the area of each individual square and then sum them up.
The area of a square is calculated by multiplying the length of its side by itself.
The given information states that there are 3 small squares with a side length of s. So, the area of each small square is s^2.
Similarly, there are 2 large squares with a side length of S. Therefore, the area of each large square is S^2.
To find the total area of the sign, we need to add up the areas of all the squares:
Area = 3 small squares + 2 large squares
Area = 3s^2 + 2S^2
Therefore, the correct expression to find the total area of the sign that needs to be painted is option A) 2S^2 + 3s^2.
The total area of the sign that needs to be painted can be calculated by adding the areas of the small squares and the large squares.
The area of a square is given by the formula A = s^2, where s is the side length.
So, the area of one small square is s^2, and since there are 3 small squares, the total area of the small squares is 3s^2.
Similarly, the area of one large square is S^2, and since there are 2 large squares, the total area of the large squares is 2S^2.
Therefore, the expression to find the total area of the sign that needs to be painted is 3s^2 + 2S^2.
Hence, the correct answer is B) 3S^2 + 2s^2.