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