Download Area of Regular Polygons

Area of Regular Polygons
Brett Solberg AHS
‘11-’12
Warm-up
 1) What is the measure of an interior angle in a regular
hexagon?
hint (n-2)*180
 2) Find the value of x and y in the regular triangle.
 Which HW problems should we review?
Today’s Agenda
 Mini-Quiz
 Area of Regular Polygons
 finding interior angles
 finding angles created by radii
 using apothem
 applying properties of special right triangles
 Announcements
 4th Quarter Change – Only one retake for the quarter
Regular Polygon
 What is a polygon?
 an enclosed figure with at least 3 straight sides.
 What is a regular polygon?
 a polygon where all the sides and angles are congruent
Radius and Apothem
 Any regular polygon can be circumscribed.
 Radius: distance from the center to the vertex.
 Apothem: perpendicular distance from the center to a side.
 Draw and label the other radii and apothems.
Area of a Regular Polygon
 The area of a regular polygon is half the product of the
apothem and the perimeter.
 How do we find perimeter?
 p = ns
 n= number of sides
 s = length of one side
Example 1
 Find the area of a regular decagon with a 12.3 inch apothem
and a side length of 8.
 Decagon =
 Perimeter =
 Area =
Example 2
 Find the area of a regular polygon with twenty 12 inch sides
and a 37.9 inch apothem.
 Perimeter =
 Area =
Area of a Polygon
 What if we aren’t given the apothem?
 fill in missing angles
 use properties of special right triangles
30
60
Equilateral Triangle
 Label the radii and apothems.
 What angles do they create?
Square
 Label the radii and apothems.
 What angles do they create?
Example 1 – Regular Pentagon
 Label the radii and apothem
 Find the angles in the regular pentagon.
Regular Hexagon
 Label the radii and apothem
 Find the angles in the regular pentagon.
Example 3
 Find the area of a regular triangle with a side of 8 inches.
in
Example 4
 Find the area of a square with the radius of 8 cm.
Homework
 10-3 Worksheet