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.
Exploration
- Slide the slider to unravel the circle. Explain how the width of the shape relates to the circumference of the circle.
- 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.
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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.
$\text{Area of a circle}=\pi r^2$Area of a circle=πr2
Practice questions
QUESTION 1
Find the area of the circle shown, correct to one decimal place.
QUESTION 2
If the diameter of the circle is $24$24 cm, find its area correct to one decimal place.
QUESTION 3
If the radius of the circle is $9$9 cm, find its area correct to two decimal places.