Regular Polygons and Their Properties

This video tutorial covers the calculation of the area of regular polygons using three examples: a hexagon with a given side length, a pentagon with a given apothem, and a decagon inscribed in a circle with a given radius. The video explains the relevant formulas and demonstrates the use of geometry and trigonometry to find the area. It emphasizes understanding the properties of regular polygons and the application of trigonometric ratios to solve for unknowns.

What are the three types of given information used in the examples to find the area of a regular polygon?

• Angle, side length, and height

• Side length, radius, and apothem

• Diameter, height, and base

• Perimeter, area, and volume

Which formula is used to find the area of a regular polygon when given the apothem and perimeter?

• Perimeter squared

• One-half the apothem times the perimeter

• Base times height

• One-half the base times the height

What makes a polygon 'regular'?

• All interior angles and side lengths are the same

• All sides are parallel

• It has at least four sides

• It has no right angles

In a regular hexagon with a side length of 10 cm, what is the measure of each central angle?

• 90 degrees

• 60 degrees

• 30 degrees

• 45 degrees

What is the length of the apothem in a regular hexagon with a side length of 10 cm?

• 10√3 cm

• 5 cm

• 10 cm

• 5√3 cm

For a regular pentagon with an apothem of 4 inches, what is the measure of each central angle?

• 45 degrees

• 90 degrees

• 36 degrees

• 72 degrees

How do you find the perimeter of a regular pentagon if you know the length of one side?

• Square the side length

• Divide the side length by 5

• Multiply the side length by 4

• Multiply the side length by 5

What is the radius of the circle in which a regular decagon is inscribed?

• 5 meters

• 12 meters

• 10 meters

• 8 meters

How do you find the central angle of a regular decagon?

• Multiply 180 degrees by 10

• Divide 180 degrees by 10

• Divide 360 degrees by 10

• Multiply 360 degrees by 10

What trigonometric function is used to find the apothem in a regular decagon?

• Secant

• Cosine

• Sine

• Tangent