How do you find the diameter of a circle given its area?

To find the diameter of a circle given its area, use the formula: diameter = 2 × √(area/π).

To start, recall that the area of a circle is given by the formula A = πr², where A is the area and r is the radius. To find the radius from the area, you need to rearrange this formula to solve for r. Divide both sides of the equation by π to get r² = A/π. Next, take the square root of both sides to find r, which gives r = √(A/π).

Once you have the radius, finding the diameter is straightforward. The diameter of a circle is simply twice the radius, as the diameter spans the entire width of the circle, passing through the centre. Therefore, multiply the radius by 2 to get the diameter. This gives you the formula: diameter = 2 × √(A/π).

For example, if the area of a circle is 50 square centimetres, you would first calculate the radius by finding √(50/π). Using a calculator, √(50/π) is approximately 3.99 cm. Then, multiply this radius by 2 to get the diameter, which is approximately 7.98 cm.

This method ensures you can accurately determine the diameter from any given area, using basic algebra and understanding of circle properties.