Geometry / Unit 11: Area, Surface Area and Volume
11.2 Area of Circles and Composite Figures
Notes
- Circle: $A = \pi r^2$. Use the radius, not the diameter.
- A composite figure is made of simpler shapes. Add the pieces, or subtract the parts cut out.
- For a shaded region, find the area of the whole and subtract the unshaded part.
- Example: a 10 by 10 square with a circle of radius 5 inside it. The area outside the circle is $100 - 25\pi \approx 21.5$.
Practice
A circle has a diameter of 12. Find its area.
$r = 6$, so $A = 36\pi$.
A window is a 10 by 6 rectangle with a semicircle on top whose diameter is the 6-unit side. Find its total area.
Semicircle: $\displaystyle \frac{1}{2}\pi(3)^2 = 4.5\pi$.
A circular table of radius 2 feet sits on a 6 by 8 foot rug. How much rug area is not under the table, to the nearest tenth?
$48 - 4\pi \approx 48 - 12.57 = 35.4$.
Ready for more? Take the Unit 11 test.