Geometry_8.3_March 22-23
8.3 Area of Regular Polygons
(using Pythagorean Theorem)
Learning Target: I can find 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.
(called radius of reg. polygon)
What do you notice about the
triangles made?
So... how should we find the area of a regular polygon?
1
Geometry_8.3_March 22-23
To find the area of a regular polygon:
1. Draw the isosceles ∆s.
2. Find the height and base of the the isosceles ∆.
(apothem)
3. Find the
area
of one isosceles ∆.
4. Multiply by the number of ∆'s to find the area of the regular polygon.
Area of regular polygon =
Area of isosceles ∆ • Number of ∆'s
(number of ∆s = sides of polygon)
In the regular polygon,
a) find the area of the isosceles triangle (draw all the radii)
b) state the number of isosceles triangles
c) area of the entire polygon.
1.
apothem (h)
19
22
6
Area of isosceles ∆ = ______ # of ∆s____ Area of polygon= _______
2
Geometry_8.3_March 22-23
In the regular polygon, a) find the area of the isosceles triangle (draw all the radii)
sides and ∠'s are ≅
b) state the number of isosceles triangles
c) area of the entire polygon.
2. Perimeter = 192
8 ∆'s
29
2,784
Area of isosceles ∆ = ______ # of ∆s____ Area of polygon= _______
In the regular polygon, a)find the value of x
c) state the number of isosceles triangles
b) find the area of the isosceles ∆
d) area of the entire polygon.
3.
x
26
38
x = ____
9 ∆'s
9
464.1 # of ∆s____
Area of isosceles ∆ = ______
Area of polygon= _______
3
Geometry_8.3_March 22-23
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.
4.
46
37.2
x
x = ____
Area of isosceles ∆ = ______ # of ∆s____ Area of polygon= _______
Assignment: 8.3 Worksheet
8.3 Worksheet
selected answers
1c.) A = 7,350 units2
3c.) A = 17,466 units2
4
Geometry
8.3 Area of Regular Polygons (with Pythagorean Theorem)
Name________________________________Pd.___
Show work! In the following regular polygons, find the…
a) area of the isosceles triangle b) number of isosceles triangles, and c) area of the entire regular polygon.
1.
a) Area of isosceles ∆ = ________
b) # of isosceles ∆s = ________
c) Area of polygon = ________
a) Area of isosceles ∆ = ________
b) # of isosceles ∆s = ________
c) Area of polygon = ________
2.
Show work! In the following regular polygons, find the…
a) value of x, b) area of the isosceles ∆, c) number of isosceles ∆s, and d) area of the regular polygon.
3.
a) x = _______ b) Area of
= _________ c) # of isosceles ∆s = ______ d) Area of = _________
isosceles ∆
polygon
4.
a) x = _______ b) Area of
= _________ c) # of isosceles ∆s = ______ d) Area of = _________
isosceles ∆
polygon