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Finding the area of regular polygons

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Finding the area of regular polygons

- Review of Prior Knowledge
- Regular Polygon: a polygon in which all sides and angles are congruent.

- New Vocabulary
- Radius – a line connecting the center of a polygon with a vertex.
- Apothem – a line connecting the center of a polygon with a midpoint of one of the sides which functions as a perpendicular bisector

radius

apothem

Step 1: Break the polygon into triangles. Draw in the radii and one apothem.

Step 2: Remove one triangle from the polygon.

Step 3: Find lots of angles!! Transfer them onto the triangle.

Step 4: Find the sides of the triangle using special rules.

Step 5: Find the area of the yellow triangle…

Step 6: So, the total area = 6 ( ) = sq units

360

There are 6 triangles in a hexagon so in order to find each angle in the center divide 360 by 6. Each is 60.

60

60

60

10

The 60 on top of the triangle needs to be split in two equal parts.

30

30

5

5

Area = ½ (10)( ) =

10

There are 6 of these triangles.

1. Break the polygon into triangles by drawing in the radii.

2. Remove one triangle from the polygon

3. Fill in lots of angles.

4. Find the area of the removed triangle byfinding the base and height of the triangle.

5. Find the area of the entire polygon by multiple the area of one triangle by the number of triangles.

Area of triangle = ½ ( )(4) =

Area of polygon = (# of triangles)(area of yellow triangle)

= 3 ( ) = square units

360 / 3 = 120

120

120

120

4

Use the 30-60-90 rules

60

60

4

30

30

Area = 128 square units

8

Area = square units

6

Area = square units

4

Area =(# of tri’s)(area of one tri)

(# of tri’s) = (# of sides) so…

Area =(# of sides)(area of one tri)

(area of one tri) = ½ bh so…

Area =(# of sides)( ½ bh)

we can multiply in any order so…

Area = ½ (h) (# of sides)(b)

the height (h) is the same as the apothem so…

Area = ½ (a) (# of sides)(b)

(# of sides)(base) = the perimeter so…

Area = ½ (a) (p)

h=a