Given square:
Perimeter: Let the side length of the given square be x.
Perimeter = 4x
Area: Area = x^2
Dilated square:
Perimeter: Since the scale factor is 3, the side length of the dilated square will be 3x.
Perimeter = 4(3x) = 12x
Area: Area = (3x)^2 = 9x^2
Calculations:
Given square:
Perimeter = 4x, so the perimeter is 4 times the side length. As the side length is unknown in this specific case, we cannot calculate the perimeter without additional information.
Area = x^2
Dilated square:
Perimeter = 12x, which is 3 times the perimeter of the original square.
Area = 9x^2, which is 9 times the area of the original square.
The square below is dilated by a scale factor of 33. Find the perimeter and area of the square below, as well as the perimeter and area of the dilated square. Express your answers as whole numbers, decimals, or fractions in simplest terms (no mixed numbers). Figures are not necessarily drawn to scale.
Perimeter of given square ____
Area of given square ____
Perimeter of dilated square____
Area of dilated square____
3 answers
side length is 8
Given square:
Side length = 8 units
Perimeter = 4 * 8 = 32 units
Area = 8^2 = 64 square units
Dilated square:
Side length = 8 * 3 = 24 units
Perimeter = 4 * 24 = 96 units
Area = 24^2 = 576 square units
So, the answers are:
Perimeter of given square: 32 units
Area of given square: 64 square units
Perimeter of dilated square: 96 units
Area of dilated square: 576 square units
Side length = 8 units
Perimeter = 4 * 8 = 32 units
Area = 8^2 = 64 square units
Dilated square:
Side length = 8 * 3 = 24 units
Perimeter = 4 * 24 = 96 units
Area = 24^2 = 576 square units
So, the answers are:
Perimeter of given square: 32 units
Area of given square: 64 square units
Perimeter of dilated square: 96 units
Area of dilated square: 576 square units
1 answer