Lesson 11.2 Extra Notes on the Areas of Regular Polygons
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| Area of a triangle = | ½ bh
where b is the base and a is the altitude perpendicular to that base
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| The radius of a polygon is the same as the radius a what? | circle
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| The endpoints of a radius are the what? | the center and a vertex of the polygon.
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| Every radius in the same polygon or circle is | congruent
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| Since the radii are all the same and each radius is a side of a triangle in the regular polygon, then? | The two consecutive radii are the legs of an isosceles triangle.
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| Every n-gon can be divided into what? | n congruent isosceles triangles.
(n = number of sides)
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| The area of any regular polygon is what? | n times the area of one of those isosceles triangles.
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| The apothem of a regular polygon is the same as what? | The same as the altitude as the isosceles triangle.
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| The endpoints of the apothem are what? | The center of the polygon and the midpoint of a side.
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| Area of a regular polygon = | n(area of a triangle)
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| where n = | number of sides
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| (Area of any Regular Polygon) The base b of the triangle is what? | the same as the side s of the polygon.
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| The height h of the triangle is what? | the same as the apothem a of the polygon.
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| A = ? | n ∙ (area of the isosceles triangle) or
n ∙ ( ½ b ∙ h) or
n ∙ ( ½ s ∙ a) or
½ a ∙ ns or
½ a ∙ P where P is the Perimeter of the polygon
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