topic badge

7.04 Area of a circle


We already know that area is the space inside a 2D shape.  We can find the area of a circle, but we will need a special rule.  

Let's look at what happens when we unravel segments of a circle.  


  1. Slide the slider to unravel the circle. Explain how the width of the shape relates to the circumference of the circle.
  2. Move the triangle to slide the triangle together. What figure is formed? Explain how the area of this figure relates to the area of the circle.

Interesting isn't it that when we realign the segments we end up with a parallelogram shape.  Which is great, because it means we know how to find the area based on our knowledge that the area of a parallelogram has formula $A=bh$A=bh.  In a circle, the base is half the circumference and the height is the radius.  


Area of a Circle

$\text{Area of a circle}=\pi r^2$Area of a circle=πr2

Practice questions


Find the area of the circle shown, correct to one decimal place.

A circle with a radius labeled 6 cm. The radius is drawn as an arrow starting from the center point and with its arrowhead touching the circumference.


If the diameter of the circle is $24$24 cm, find its area correct to one decimal place.


If the radius of the circle is $9$9 cm, find its area correct to two decimal places.



Understand and use the formulas for the area and circumference of a circle to solve problems; give an informal derivation of the relationship between the circumference and area of a circle.

What is Mathspace

About Mathspace