To find the area of the dilated square, we first need to understand how dilation affects the area of a shape. When a shape is dilated by a certain factor, the lengths of its sides are multiplied by that factor, and the area is multiplied by the square of that factor.
In this case, the original area of the square is 4 in². The dilation factor is 7. To find the area of the dilated square, we’ll calculate the square of the dilation factor:
Square of the dilation factor: 7 × 7 = 49
Next, we multiply the original area by this squared factor:
Dilated area = Original area × (Dilation factor)²
Dilated area = 4 in² × 49 = 196 in²
Thus, the area of the dilated square is 196 in².