What is the area of a similar shape with sides doubled?

The area of a similar shape with sides doubled is four times the original area.

When you double the sides of a shape, you are scaling the shape by a factor of 2. For similar shapes, the area scales by the square of the scale factor. This means if the scale factor is 2, you square it (2^2) to get 4. Therefore, the area of the new shape is four times the area of the original shape.

Let's consider a simple example. Suppose you have a square with a side length of 3 units. The area of this square is calculated as side length squared, which is 3^2 = 9 square units. If you double the side length, the new side length becomes 6 units. The area of the new square is 6^2 = 36 square units. Notice that 36 is four times 9, confirming that the area has increased by a factor of 4.

This principle applies to all similar shapes, not just squares. For instance, if you have a triangle with a base of 4 units and a height of 3 units, its area is 1/2 * base * height = 1/2 * 4 * 3 = 6 square units. Doubling the sides means the base becomes 8 units and the height becomes 6 units. The area of the new triangle is 1/2 * 8 * 6 = 24 square units, which is again four times the original area.

Understanding this concept is crucial for solving problems involving similar shapes and their areas in GCSE Maths.