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Math · 35 · Geometry and Trigonometry

Polygons

Notes

Key points

  • Interior sum (n−2)⋅180∘(n-2)\cdot180^\circ — not on the reference sheet.
  • Exterior angles always sum to 360∘360^\circ, for any nn.
  • Regular polygon: all sides equal and all angles equal.
  • Interior + exterior at one vertex = 180∘180^\circ.
  • Why n−2n-2: diagonals from one vertex cut it into n−2n-2 triangles.
  • Regular hexagon = 6 equilateral triangles.

Formulas

Interior angle sumS=(n−2)⋅180∘S=(n-2)\cdot180^\circNot on the reference sheet
Regular interior angle(n−2)⋅180∘n\dfrac{(n-2)\cdot180^\circ}{n}
Regular exterior angle360∘n\dfrac{360^\circ}{n}
Number of sidesn=360∘exterior anglen=\dfrac{360^\circ}{\text{exterior angle}}
Regular hexagon areaA=6⋅34s2=332s2A=6\cdot\dfrac{\sqrt{3}}{4}s^2=\dfrac{3\sqrt{3}}{2}s^2

Common traps

  • Using n⋅180∘n\cdot180^\circ instead of (n−2)⋅180∘(n-2)\cdot180^\circ.
  • Dividing the angle sum by n when the polygon is not regular.
  • Giving the exterior angle when the question asks for the interior.

SAT tip

Given one angle of a regular polygon: exterior = 180° − interior, then n = 360° ÷ exterior.

Test yourself

10 official SAT questions on Polygons, easiest first.

    Next lesson36 · 3D Shapes