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# Area of a Circle Using the Diameter

(KS3, Year 7)

## The Lesson

The 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:

## Interactive Widget

Use this**interactive widget**to draw a circle and then calculate its area from the diameter. Start by clicking in the shaded area.

**Diameter**

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**Radius (diameter ÷ 2)**

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## How to Find the Area of a Circle Using the Diameter

Finding the area of a circle using the diameter is easy.## Question

What is the area of a circle with a diameter of 10 cm, as shown below?## Step-by-Step:

# 1

# 2

Substitute the diameter into the formula. In our example, d = 10.

Area = π × 10^{2}⁄4

Area = π × 10 × 10 ÷ 4

Area = π × 100 ÷ 4

Area = π × 25

Area = 3.14 × 25

Area = 78.5 cm^{2}

## Answer:

The area of the circle with a diameter of 10 cm is 78.5 cm^{2}.

## How to Find the Area of a Circle Using the Radius

The 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

**for**

^{d}⁄_{2}**r**:

The

**in the brackets is being squared. When a fraction is squared, both the numerator and the denominator are squared:**

^{d}⁄_{2}This is is formula for the area of a circle using the diameter.

## A Note on Units

The area of a circle is a length times a length, so we say its dimension is length^{2}. (All areas are lengths squared). This affects the units used. If the diameter is in cm, the area is in cm

^{2}. If it is in inches, the area is in inches

^{2}.

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