The LessonThe area of a circle is found using the formula:
In this formula, d is the diameter of the circle. The image below shows what we mean by diameter:
How to Find the Area of a Circle Using the DiameterFinding the area of a circle using the diameter is easy.
QuestionWhat is the area of a circle with a diameter of 10 cm, as shown below?
Substitute the diameter into the formula. In our example, d = 10.
Area = π × 102⁄4
Area = π × 10 × 10 ÷ 4
Area = π × 100 ÷ 4
Area = π × 25
Area = 3.14 × 25
Area = 78.5 cm2
Answer:The area of the circle with a diameter of 10 cm is 78.5 cm2.
Lesson SlidesThe slider below shows another real example of how to find the area of a circle using the diameter. Open the slider in a new tab
How to Find the Area of a Circle Using the RadiusThe area of a circle can be found using the radius rather than the diameter. The area of a circle, using the radius, is found using the formula:
In the formula, r is the radius of the circle. The image below shows what we mean by radius:
Read more about how to find the area of a circle using the radius
What Is a Circle?A circle is a shape containing a set of points that are all the same distance from a given point, its center.
Why Does This Formula Work?The formula for the area of a circle is better known in terms of the radius:
The radius can be found from the diameter. The radius is half the length of the diameter:
Substitute d⁄2 for r:
The d⁄2 in the brackets is being squared. When a fraction is squared, both the numerator and the denominator are squared:
This is is formula for the area of a circle using the diameter.