To find the total area of the sign that needs to be painted, we need to calculate the area for both the small and large squares.
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Area of one small square: The area \( A_s \) of one small square is given by the formula: \[ A_s = X^2 \]
Since there are 3 small squares, the total area for the small squares \( A_{small} \) is: \[ A_{small} = 3 \times A_s = 3 \times X^2 = 3X^2 \]
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Area of one large square: The area \( A_l \) of one large square is given by the formula: \[ A_l = Y^2 \]
Since there are 4 large squares, the total area for the large squares \( A_{large} \) is: \[ A_{large} = 4 \times A_l = 4 \times Y^2 = 4Y^2 \]
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Total area of the sign: To find the total area that needs to be painted \( A_{total} \), we sum the areas of the small and large squares: \[ A_{total} = A_{small} + A_{large} = 3X^2 + 4Y^2 \]
Thus, the expression for the total area of the sign that needs to be painted is: \[ A_{total} = 3X^2 + 4Y^2 \]
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