Warm up

• Find x and y.•

Find the square footage of a regular polygon

• A special stage will be build for Justin Bieber’s concert. You are hired to decorate the stage. But first, you have to measure the square footage of the floor, which is in the shape of a regular hexagon. What’s your strategy to find the area?

• (hint: break it into smaller polygons)

Definition of a regular polygon

• What is a regular polygon?• A polygon is regular when all angles are equal and all sides

are equal (otherwise it is "irregular")• What is a center, a radius, and an apothem of a polygon?

Center

radius

apothem

• Before you get a chance to measure the stage, you get a call from the owner saying that he knows that every side of the stage is 8ft and the apothem is 4 Can you find the total area of the stage?

Area of a regular polygon

A (area) = n·(1/2)·a·sp (perimeter) = n·sA = ·a·p

Wait a minute…• You are about to order the material, but the owner calls

again telling you to ignore the previous measurements. He is sure the sides are 10 ft, but not sure about the apothem. Can you find the area?

• (hint: use angle measurement.)

More practice !!What are the areas of each regular polygon?

Just two more!!• What are the areas of each regular polygon?