# Area of a Circle

Lesson

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.

The following investigation will demonstrate what happens when we unravel segments of a 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

#### Worked Examples

##### QUESTION 1

If the radius of the circle is $5$5 cm, find its area.

##### QUESTION 2

Find the area of the shaded region in the following figure, correct to 1 decimal place.

##### QUESTION 3

Find the area of the shaded region in the following figure, correct to 1 decimal place.

### Outcomes

#### GM5-4

Find the perimeters and areas of circles and composite shapes and the volumes of prisms, including cylinders