Math 6 B Unit 6 Lesson 5: Area of Polygons
In this lesson, we will learn about the area of polygons. A polygon is a closed shape with straight sides. The area of a polygon is the space inside the shape.
To find the area of a polygon, we can use the formula:
Area = 1/2 x Perimeter x Apothem
Where:
- Perimeter is the sum of the lengths of all the sides of the polygon
- Apothem is the line segment from the center of the polygon to the midpoint of one of its sides
Let's work through an example:
Example:
Find the area of a regular hexagon with a side length of 6 units.
1. First, let's find the perimeter of the hexagon. Since a hexagon has 6 sides, the perimeter is:
Perimeter = 6 x 6 = 36 units
2. Next, let's find the apothem of the hexagon. The apothem of a regular hexagon can be found using the formula:
Apothem = (square root of 3) / 2 x side length
Apothem = (square root of 3) / 2 x 6
Apothem = 3 square root of 3 units
3. Now that we have the perimeter and apothem, we can find the area of the hexagon:
Area = 1/2 x 36 x 3 square root of 3
Area = 18 x 3 square root of 3
Area = 54 square root of 3 square units
Therefore, the area of the regular hexagon with a side length of 6 units is 54 square root of 3 square units.