Composite Figures and Regular Polygons

This video tutorial covers the areas of regular polygons and composite figures. It explains the properties of regular polygons, such as pentagons and hexagons, and demonstrates how to calculate their areas using formulas involving perimeter and apothem. The tutorial also includes examples of finding the area of an equilateral triangle and a regular pentagon with a given radius. Additionally, it discusses composite figures, which are made up of smaller known shapes, and how to calculate their total area by summing the areas of these shapes.

What is the center of a regular pentagon inscribed in a circle?

• The midpoint of a side

• The center of the circle

• A vertex of the pentagon

• The intersection of diagonals

How is the apothem of a regular polygon defined?

• A line from a vertex to the center

• A line from a vertex to the midpoint of the opposite side

• A line from the center perpendicular to a side

• A line from the center to a vertex

What is the measure of a central angle in a regular pentagon?

• 60 degrees

• 108 degrees

• 72 degrees

• 90 degrees

Which formula is used to calculate the area of a regular polygon?

• Area = pi x radius^2

• Area = side^2

• Area = 1/2 x perimeter x apothem

• Area = base x height

What is the perimeter of an equilateral triangle with side length 6 inches?

• 12 inches

• 18 inches

• 24 inches

• 30 inches

In a regular hexagon, how many equilateral triangles can it be divided into?

• 3

• 5

• 4

• 6

What is the length of one side of a regular hexagon if the apothem is 6 inches?

• 4√3 inches

• 6 inches

• 10 inches

• 8 inches

How do you find the area of a regular pentagon with a given radius?

• Use the formula for a circle

• Use trigonometry to find the apothem and side length

• Use the formula for a triangle

• Use the formula for a rectangle

What is a composite figure?

• A figure with equal sides

• A figure with only straight sides

• A figure made up of smaller known shapes

• A figure with curved sides

How do you find the area of a composite figure?

• Divide the area by the number of shapes

• Multiply the areas of all shapes

• Subtract the areas of all shapes

• Add the areas of all smaller shapes