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.
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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
Find the area of the circle shown, correct to one decimal place.
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.
Circles and measurement: a. Know that a circle is a two-dimensional shape created by connecting all of the points equidistant from a fixed point called the center of the circle. b. Understand and describe the relationships among the radius, diameter, and circumference of a circle. c. Understand and describe the relationship among the radius, diameter, and area of a circle. d. Know the formulas for the area and circumference of a circle and solve problems. e. Give an informal derivation of the relationship between the circumference and area of a circle.