Module 4 · Geometry
Chapter 45: Polygons
Geometry
3 topics
What this chapter covers
The 3 topics below make up Polygons on the CAT. Click any topic to open its notes, examples and practice test.
Study material & tests
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8 auto-graded questions per topic, pulled from the question bank.
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📝 Chapter test
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Formula Reference Sheet
This chapter
Angles in a polygon
| Sum of interior angles | (n − 2) × 180° |
|---|---|
| Each interior angle (regular) | (n − 2) × 180° / n |
| Sum of exterior angles | 360° (any convex polygon) |
| Each exterior angle (regular) | 360° / n |
| Interior + exterior (at a vertex) | 180° |
Diagonals & area
| Number of diagonals | n(n − 3) / 2 |
|---|---|
| Sides from interior angle | n = 360 / (180 − interior) |
| Area of a regular polygon | (1/2) × perimeter × apothem |
| Area via side a | (n a² / 4) × cot(180°/n) |
| Area of a regular hexagon | (3√3 / 2) × a² |
CAT reference
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