11.2a Area of Regular Polygons

CCSS LESSON GOALS Understand that to find the

area of a regular polygon you find the area of one triangle and multiply that area by the number of sides the polygon has.

ESLRs: Becoming Effective Communicators, Competent Learners and Complex Thinkers

G GPE 7: Use coordinates to compute perimeters of polygons and areas of triangles and rectangles, e.g., using the distance formula.

definition

Center of a Polygon is the center of its circumscribed circle.

Radius of a Polygon is the radius of its circumscribed circle.

definition

The Apothem of a Polygon is the distance from the center to any side of the polygon.

radius

apothem

definition

Central Angle of a Regular Polygonis an angle whose vertex is the center and whose sidescontain two consecutive vertices of the polygon.

definition

The Measure of a Central Angle of a Regular Polygon

72o 360

n

360

5

ExampleFind the area of the triangle.

12A bh

12 2 3

3 square units1

3

Example

12A bh

12 6 3 3

9 3 square units

3 3

3

Find the area of the triangle.

Area of a Regular Polygon1. Divide the polygon into congruent triangles by drawing

the radii of the polygon

2. Find the measure of the central angle.

3. Draw the apothem.What happens to the central angle?

4. Find the length of the apothem

5. Find the area of one inner triangle.

6. Multiply by the number of sides.

Area of a Regular PolygonFind the area of a regular hexagon with side length of 4 yds.

1. Divide the polygon into congruent triangles by drawing the radii of the polygon.

4 yds

360

6

Area of a Regular Polygon

2. Find the measure of the central angle.

360

n

60

4 yds

Find the area of a regular hexagon with side length of 4 yds.

Area of a Regular Polygon

3. Draw the apothem.

60

What happens to the central angle?

12 6030

4 yds

Find the area of a regular hexagon with side length of 4 yds.

Area of a Regular Polygon

What happens to the base?

12 42 yds

30

4 yds

3. Draw the apothem.

Find the area of a regular hexagon with side length of 4 yds.

Area of a Regular Polygon

4. Find the length of the apothem.

30

22 3

4 yds

Find the area of a regular hexagon with side length of 4 yds.

4 yds

Area of a Regular Polygon5. Find the area of one inner triangle.

12 4 2 3A

2 3

4 3

4 yds

Find the area of a regular hexagon with side length of 4 yds.

Area of a Regular Polygon6. Multiply by the number of sides/triangles.

6 4 3A

4 yds

224 3 yd

4 3

4 yds

Find the area of a regular hexagon with side length of 4 yds.

Area of a Regular PolygonFind the area of a square with a radius 6 units.

1. Divide the polygon into congruent triangles by drawing the radii of the polygon.

Area of a Regular Polygon

2. Find the measure of the central angle.

Find the area of a square with a radius 6 units.

Area of a Regular Polygon

3. Draw the apothem.What happens to the central angle?

Find the area of a square with a radius 6 units

Area of a Regular Polygon

4. Find the length of the apothem.

Find the area of a square with a radius 6 units

2

2

Area of a Regular Polygon5. Find the area of one inner triangle.

Find the area of a square with a radius 6 units

18A

Area of a Regular Polygon6. Multiply by the number of sides/triangles.

4 18A

272 units

Find the area of a square with a radius 6 units.

Area of a Regular PolygonThe area of a regular polygon can be found using

n = the number of sidess = the length of a sidea = the length of the apothem

a = the length of the apothem P= perimeter of the polygon

Today’s Assignment #3

p.672: 1 – 5, 9, 10, 16, 18, 22, 30