Measurement

Hong Kong

Stage 1 - Stage 3

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`=`b``h`. 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=π`r`2

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

Give your answer as an exact value.

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

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