section 7 –5 areas of regular polygons objectives: to find the area of a regular polygon
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Radius: Distance from the center to a vertex.Apothem: Perpendicular distance from center to a side.
Regular Polygons
Example 1 Finding Angle Measures
A) The figure below is a regular pentagon with radii and an apothem drawn. Find the measures of each numbered angle.
The radii divide regular polygons into congruent isosceles triangles. What formula could you use to find the area of each triangle?
𝑨=𝟏𝟐𝒂𝒔
Since there are “n” congruent triangles in each regular polygon, the Area of any regular polygon would be .
How do you find perimeter of a regular polygon?
P
So you can replace the n and s in the formula with P (for perimeter) so the formula for the area of
regular polygons becomes:
Example 2 Finding the Area of a Regular Polygon
A) Find the area of a regular decagon with a 12.3 inch apothem and 8 in sides.
Example 3 Finding the Area of a Regular Polygon (finding Apothem)
A) Find the area of the regular hexagon below.
Example 4 Finding the Area of an Equilateral Triangle
A) Find the area of the equilateral triangle below.
B) Find the area of an equilateral triangle with apothem 8 cm. Leave your answer in simplest radical form.
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