1. Area of Polygons and Circles
8.1
Area of Polygons and Circles
Objectives:
To find area of polygons and circles.

2. Definitions Any side of the parallelogram can be called the base.
Every base has a corresponding altitude.
The length of an altitude is called the height of the parallelogram.

3. Area
What is area?
How many unit squares will fit into the shape, no matter how complicated the shape.
Area is a two dimensional measurement.

4. Area of a Parallelogram
If a parallelogram has an area of A square units, a base of b units, and height of h units, then A = bh.

5. Area of a Triangle
If a triangle has an area of A square units, a base of b units, and corresponding height of h units, then h b

6. Area of a Triangle Animation

7. Area of a Trapezoid
If a trapezoid has an area of A square units, bases of b1 units and b2 units, and height of h units, then b1 b2 h b2 b1

8. Area of a Trapezoid Animation

9. Area of a Rhombus
If a rhombus has an area of A square units and diagonals of d1 and d2, then d1 d2

10. Apothem
A segment drawn from the center of a regular polygon perpendicular to a side is called an apothem.

11. Area of a Regular Polygon
If a regular polygon has an area of A square units, a perimeter of P units, and an apothem of a units, then a

12. a a P

13. Example
Find the apothem, area, and perimeter of each regular polygon. Round to the nearest tenth.

14. Example
Find the apothem, area, and perimeter of each regular polygon. Round to the nearest tenth.

15. Example
Find the area of the figure. Round to the tenths place if needed.
Perimeter = 40

16. Area of a Circle
If a circle has an area of A square units and a radius of r units, then r

17. Steps to Solve Area Problems
Identify Shape
Write down complete formula
Substitute information into formula
Solve (i.e. do the math)

18. In Class Examples

19. Homework
8.1 Worksheet