Find the Area of a Regular Polygon Given Radius or Apothem or Side

Master finding the area of regular polygons with this comprehensive math tutorial! Mario's Math Tutoring walks you through three distinct examples: given the side length, given the apothem, and given the radius. Learn the key formulas (Area = ½ * apothem * perimeter or Area = ½ * apothem * n * side length) and understand how they're derived from subdividing polygons into congruent triangles. We'll use special right triangles (30-60-90) and trigonometry (sine, cosine, tangent) to find missing dimensions like the apothem and side length. Perfect for geometry students!

Timestamps:

0:00 Introduction to Area of Regular Polygons
0:20 Formulas for Area of Regular Polygons (½aP or ½anS)
0:40 Derivation of the Area Formulas (Subdividing into Triangles)
1:30 Example 1: Given Side Length (Regular Hexagon with Side = 10cm)
2:00 Finding the Central Angle (360°/n)
2:20 Dropping the Apothem (Creating 30-60-90 Triangles)
2:50 Using 30-60-90 Special Right Triangle Ratios to find Apothem
3:50 Calculating Area using Apothem and Perimeter
4:30 Alternative: Using Trigonometry (Tangent) to find Apothem
5:20 Example 2: Given Apothem (Regular Pentagon with Apothem = 4 inches)
5:40 Finding the Central Angle & Half Angle
6:00 Using Trigonometry (Tangent) to find Half Side Length
6:40 Calculating Perimeter
7:00 Calculating Area using Apothem and Perimeter
7:40 Tip: Carry Decimal Values for Accuracy
8:20 Example 3: Given Radius (Regular Decagon with Radius = 8 meters)
8:50 Understanding "Inscribed" and the Radius
9:20 Finding the Central Angle & Half Angle
9:50 Using Trigonometry (Cosine) to find Apothem
10:40 Using Trigonometry (Sine) to find Half Side Length
11:10 Calculating Perimeter and Area
12:00 Conclusion & More Practice
#AreaOfRegularPolygons #RegularPolygons #Geometry #MathTutorial #Apothem #Perimeter #Radius #SpecialRightTriangles #Trigonometry #MathHelp #mariosmathtutoring

➡️JOIN the channel as a CHANNEL MEMBER at the "ADDITIONAL VIDEOS" level to get access to my math video courses(Algebra 1, Algebra 2/College Algebra, Geometry, and PreCalculus), midterm & final exam reviews, ACT and SAT prep videos and more! (Over 390+ videos)
   / @mariosmathtutoring