5.1 Polygon Sum Conjecture. Angle Exploration Equilateral Triangle 60°
Given a regular polygon, you can find its area by dividing the polygon into congruent, non-...
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Transcript of Given a regular polygon, you can find its area by dividing the polygon into congruent, non-...
Given a regular polygon, you can find its area by dividing the polygon into congruent, non-overlapping, equilateral triangles.
Here a pentagon is separated into 5 congruent, non-overlapping, equilateral triangles.
In order to determine the area of this pentagon, simply determine the area of one triangle, and multiply that number by 5.
5
5
5
5
5
Altitude of a triangle.
3.44
If you have a regular polygon with n sides, you can still divide this polygon into n congruent, non-overlapping, equilateral triangles.
The area of any regular polygon can be given by the following formula.
Here, a represents the apothem of the polygon, and p represents the perimeter of the polygon.
An apothem of a polygon is the altitude of a triangle from the center of the polygon to a side of the polygon.
5
5
5
5
5
Apothem
3.44
2
2
2
2
2
2
√3
Determine the area of this hexagon.
2
2
2
2
2
2
√3
Substitute in values and simplify
Area of the hexagon
4 4
4
4
44
4
Determine the area of this heptagon.
8
Determine the area of this heptagon.
The area of the polygon in practice problem 1 is approximately 48 square units.
The area of the polygon in practice problem 2 is approximately 194 square units.