8 1 Area of Polygons and Circles Objectives

8. 1 Area of Polygons and Circles Objectives: • To find area of polygons and circles.

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.

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.

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.

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

Area of a Triangle Animation

Area of a Trapezoid • If a trapezoid has an area of A square units, bases of b 1 units and b 2 units, and height of h units, then b 1 b 2 h b 2 b 1

Area of a Trapezoid Animation

Area of a Rhombus • If a rhombus has an area of A square units and diagonals of d 1 and d 2, then d 1 d 2

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

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

a a P

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

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

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

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

Steps to Solve Area Problems 1. Identify Shape 2. Write down complete formula 3. Substitute information into formula 4. Solve (i. e. do the math)

In Class Examples

Homework 8. 1 Worksheet http: //www. idahoidea. org/Main/ISATDocuments. aspx