A square is dilated by a scale factor of 3/4 to create a new square. The area of the new square is...
To find the area of the new square created by dilating a square with a scale factor of 3/4, you need to know the area of the original square. Let's call this area A.
The scale factor represents the ratio of corresponding side lengths, so if the original square has a side length of x, then the new square will have a side length of (3/4)x.
The area of a square is calculated by multiplying the length of one side by itself. Therefore, the area of the original square is A = x * x = x^2.
To find the area of the new square, we need to determine the length of its side. Since the side length of the new square is (3/4)x, the area of the new square, let's call it A', is A' = (3/4)x * (3/4)x.
To simplify this expression, we can use the property of exponents which states that (a*b)^n = a^n * b^n. Applying this property, we have A' = (3/4)^2 * x^2.
Calculating (3/4)^2, we get (3/4)^2 = 9/16. Substituting this value back into the area equation, we have A' = (9/16) * x^2.
Therefore, the area of the new square created by dilating the original square by a scale factor of 3/4 is (9/16) times the area of the original square.
original side --- x
original area = x^2
new side = (3/4)x
new area = (9/16)x^2
so new square has area of 9/16 of the old
or
the areas of similar shapes are proportional to the square of their corresponding sides
so 3/4 ----> 3^2/4^2 = 9/16