8.3 Area of Regular Polygons(using Pythagorean Theorem)

Learning Target: I can the area of a regular polygon using pythagorean theorem. (G-MG.A.1)

Regular Polygon - a polygon that is equilateral and equiangular

Draw all the segments from center of polygon to its vertices.

So... how should we find the area of a regular polygon?

What do you notice about the triangles made?

(called radius of reg. polygon)

To find the area of a regular polygon:

1. Draw the isosceles ∆s.

2. Find the height and base of the the isosceles ∆.

3. Find the area of one isosceles ∆.

4. Find the area of the regular polygon.

Area of regular polygon =

Area of isosceles ∆ • Number of ∆s

(number of ∆s = sides of polygon)

(apothem)

In the regular polygon, a) find the area of the isosceles triangle (draw all the radii)b) state the number of isosceles trianglesc) area of the entire polygon.

1.

22

19

Area of isosceles ∆ = ______ # of ∆s____ Area of polygon= _______

24

29

2.

In the regular polygon, a) find the area of the isosceles triangle (draw all the radii)b) state the number of isosceles trianglesc) area of the entire polygon.

Area of isosceles ∆ = ______ # of ∆s____ Area of polygon= _______

3.

In the regular polygon, a)find the value of x b) find the area of the isosceles ∆ c) state the number of isosceles triangles d) area of the entire polygon.

Area of isosceles ∆ = ______ # of ∆s____ Area of polygon= _______

x 38

26

x = ____

4.

In the regular polygon, a)find the value of x b) find the area of the isosceles ∆ c) state the number of isosceles triangles d) area of the entire polygon.

Area of isosceles ∆ = ______ # of ∆s____ Area of polygon= _______

x = ____

37.246

x

Assignment: 8.3 Worksheet

Geometry - 8.3 Area of Regular Polygons

ODD worksheet answers

must show ALL work!1. c) 7350

3. d) 17,466