Deriving the Area Formula for Regular Polygons

This video tutorial explains how to find the area of regular polygons using a specific formula. It begins by defining regular polygons and the concept of an apothem. The video then derives the area formula, which involves dividing the polygon into congruent triangles. By calculating the area of one triangle and multiplying by the number of sides, the total area is found. The tutorial also explains how the formula is derived from the triangle area formula, emphasizing the role of the apothem and perimeter.

What does 'regular' mean in the context of polygons?

• All sides are of equal length and all interior angles are of the same measure.

• All sides and interior angles are of different lengths and measures.

• The polygon has an equal number of sides and angles.

• The polygon can be divided into an equal number of triangles.

What is an apothem in a regular polygon?

• The perpendicular distance from the center to a side.

• The perimeter of the polygon.

• The distance from the center to a vertex.

• The longest distance between any two vertices.

Why is the apothem considered perpendicular to the side of the polygon?

• To make the interior angles equal.

• As it ensures the shortest distance from the center to the side.

• Because it represents the radius of the polygon.

• To simplify the calculation of the area.

How is the area of a regular polygon calculated?

• Apothem times perimeter divided by 2

• Base times height

• Sum of all interior angles

• Length of one side squared

How can a regular polygon be divided for calculating its area?

• Into squares

• Into congruent triangles

• Into circles

• Into rectangles

What is the formula to find the area of a triangle?

• Base divided by height

• 1/2 base times height

• Base times height

• 1/2 base plus height

How is the area of one triangle within a regular polygon calculated?

• The length of one side times the apothem

• The base times the height divided by 2

• 1/2 the base times the height

• 1/2 the apothem times the perimeter

How does the apothem affect the calculation of a regular polygon's area?

• It has no effect on the area calculation.

• It is multiplied by the number of sides.

• It is used to calculate the perimeter.

• It is considered the height in the area formula.

What does the perimeter represent in the area formula of a regular polygon?

• The diameter of the polygon

• The length of one side of the polygon

• The distance around the polygon

• The total length of all apothems

What role does the number of sides play in calculating the area of a regular polygon?

• It is irrelevant to the area calculation.

• It is multiplied by the length of one side to find the perimeter.

• It determines the number of triangles the polygon can be divided into.

• It determines the size of each interior angle.