Area of Regular Polygons

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Presentation transcript:

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 Announcements 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.

Example 4 Find the area of a square with the radius of 8 cm. 8 cm

Homework 10-3 Worksheet