# Geometry - Area

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Geometry - Area

## 1. Regular Polygons and Circles

### 1.1. Use the Central Angle Theorem

1.1.1. Center angle = 360/n

1.1.2. n is the number of sides in the polygon

### 1.2. Use Trigonometric Ratios

1.2.1. These are necessary to find missing sides

1.2.2. Can be used with any angle given that the triangle being used includes a right angle.

### 1.3. Formulas for Regular Polygons

1.3.1. Area = (1/2)P*a

1.3.1.1. P is the perimeter

1.3.1.2. a is the apothem, a perpendicular bisector from the center to any side

### 1.4. Formula for Circles

1.4.1. Area = Pi*r^2

1.4.1.1. Pi is the greek term for ~3.14

## 3. Triangles, Trapezoids, and Rhombi

### 3.1. Triangle

3.1.1. Area = (1/2)b*h

### 3.2. Use previous formulas to derive Area of Trapezoid

3.2.1. Trapezoid=2 triangles

3.2.2. Area = (1/2)(b1+b2)*h

### 3.3. Coordinate Plane

3.3.1. Makes rhombi very simple

3.3.2. Distance formula

### 3.4. Rhombus

3.4.1. Area = (1/2)d1*d2

3.4.2. d stands for diagonal

## 4. Parallelograms

### 4.1. Using Similarity and Congruence

4.1.1. Finds sides

4.1.2. Finds angles

### 4.2. Using the Pythagorean Theorem

4.2.1. Finds missing sides

### 4.3. Using Special Triangle Theorems

4.3.1. Finds sides

4.3.2. Finds angles

### 4.4. Area = b*h

4.4.1. b is base

4.4.2. h is height

## 5. Assessment

### 5.5. Complex shapes

5.5.1. Combination of known shapes

5.5.2. Students must use critical thinking to use appropriate formulas and solve