Area of Polygons and Circles 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 b1 units and b2 units, and height of h units, then b1 b2 h b2 b1

Area of a Trapezoid Animation

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

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 Identify Shape Write down complete formula Substitute information into formula Solve (i.e. do the math)

In Class Examples

Homework 8.1 Worksheet http://www.idahoidea.org/Main/ISATDocuments.aspx