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7.04 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.  

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

Exploration

  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

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, rounded to 2 decimal places.

Outcomes

7.G.B.4

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.

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