Chapter 15: Circles 209
Here’s a way to approximate the area of the circle that’s a little easier. Cut the circle into wedges,
like a pie. Line up the wedges, alternating point up and point down. It should look like this:
The rearranged area looks a lot like a parallelogram. The height of the parallelogram is the
radius of the circle, and the base is half the circumference, or Sr. The area is base times height, or
r times Sr, which equals Sr^2. The area of a circle is the product of S and the square of the radius.
To find the area of a circle whose radius is 7 inches, you could just square 7 to get 49 and say the
area is 49S square inches. That’s absolutely true, but if you don’t really have a sense of what 49S
means, you could use^22
7
. A r^2222
7
7 154 square inches.
r
πr
CHECK POINT
- Find the area of a circle with a radius of 9 cm.
- Find the circumference of a circle with a diameter of 12 inches.
- Find the area of a circle with a diameter of 32 cm.
- Find the circumference of a circle with an area of 36S square meters.
- Find the area of a circle with a circumference of 24S feet.
Circles in the Coordinate Plane ......................................................................................
When you looked at the coordinate plane, you were interested mostly in the graphs of lines and
the connection between the line and its equation. When you draw a circle on the coordinate
plane, you can see that its equation has to be more complicated than the equation of a line,
because the pattern of where the points fall is more complicated. But it turns out that you already
know enough to figure out that equation, and it all goes back to the definition.
