A square is dilated by a scale factor of 1.25 to create a new square. How does the area of the new square compare with the area of the original shape?

Answer: the area of the new square is 1.5625 times the area of the original shape.

Justification:

Since, the square is dilated by a scale factor of 1.25 to create the new square, each side length of the new square is 1.25 times the side length of the original square. So being the area the product of two sides, the new area will be 1.25 * 1.25 = 1.5625 times the original area.

Algebraically, you can see it in this way:

Length of the sides of the original square: x Area of the original square: A = x² Length of the sides of the new square = 1.25x Area of the new square (1.25x) ² = (1.25) ² x² = (1.5625) x² = (1.5625) A

1.5625 times larger than the original

given linear factor = 1.25 then

area factor = (1.25) ² = 1.5625