Finding the Area of Regular Polygons

The video tutorial explains how to calculate the area of regular polygons using the formula: area equals one-half the apothem times the perimeter. It defines key terms like apothem and regular polygon, and demonstrates the calculation process with examples of a pentagon and a hexagon. The tutorial also includes a brief promotion of a math video course for the ACT.

What is the formula for the area of a regular polygon?

• Area = (Apothem + Perimeter) / 2

• Area = Apothem * Perimeter

• Area = Apothem + Perimeter

• Area = (Apothem * Perimeter) / 2

Tags

CCSS.6.G.A.1

What does the term 'apothem' refer to in geometry?

• The length of a side of the polygon

• The perpendicular distance from the center to a side

• The longest diagonal in the polygon

• The distance from the center to a vertex

How can regular polygons be divided to simplify area calculations?

• Cannot be divided

• Into random shapes

• Into equal triangles

• Into quadrilaterals

What trigonometric function is used to find the side length in the given example?

• Cotangent

• Sine

• Cosine

• Tangent

Tags

CCSS.HSG.SRT.C.6

What is the perimeter of the polygon in the first example?

• 29 units

• 2.9 units

• 58 units

• 14.36 units

Tags

CCSS.3.MD.D.8

What special type of triangle is used in the hexagon example?

• 45-45-90 triangle

• Equilateral triangle

• 30-60-90 triangle

• Isosceles triangle

Tags

CCSS.HSG.CO.C.10

How many triangles are formed when dividing the hexagon for area calculation?

• Three

• Four

• Five

• Six

Tags

CCSS.6.G.A.1

What is the area of the hexagon calculated in the video?

• 150 units squared

• 150 square root of 3 units squared

• 30 units squared

• 60 units squared

Tags

CCSS.6.G.A.1

What is the length of each side of the hexagon after bisecting?

• 10 units

• 30 units

• 5 units

• 5 square root of 3 units

Tags

CCSS.HSG.CO.C.9

What is the central angle of each triangle in the hexagon?

• 72 degrees

• 36 degrees

• 90 degrees

• 60 degrees