Polygons, Perimeter, Area, and Circles
Key vocabulary and formulas for plane figures, polygon angles, and circle parts.
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Questions Covered in This Set
12 cards to master
What is a polygon?
A closed flat figure made of straight line segments that meet only at their endpoints (vertices) — no curves, gaps, or crossing sides.
Interior angle sum of an n-gon
(n − 2) · 180°, because the polygon slices into n − 2 triangles from one vertex.
Each interior angle of a REGULAR n-gon
(n − 2)·180° / n. Example: regular octagon = 1080°/8 = 135°.
Sum of exterior angles of any convex polygon
Always 360°, so each exterior angle of a regular n-gon is 360°/n.
What makes a polygon 'regular' vs. just convex?
Regular = all sides equal AND all angles equal. Convex = no interior angle greater than 180°. A non-square rectangle is convex but not regular.
Area of a parallelogram and trapezoid
Parallelogram: A = bh (h is the perpendicular height, not the slanted side). Trapezoid: A = ½(b₁ + b₂)h — the average of the bases times height.
Area of a rhombus or kite
A = ½d₁d₂, half the product of the diagonals.
Area of a regular polygon
A = ½aP, where a is the apothem and P is the perimeter.
Circumference and area of a circle
C = 2πr = πd; A = πr². For r = 5 cm: C ≈ 31.4 cm, A ≈ 78.5 cm².
Arc length and sector area formulas
Arc length = (θ/360°)·2πr; Sector area = (θ/360°)·πr². Both are just a fraction of the whole circle set by the central angle.
Chord vs. tangent vs. secant
Chord: connects two points on the circle. Tangent: touches at exactly one point and is perpendicular to the radius there. Secant: cuts through the circle twice.
How do you find the area of a composite (L-shaped) figure?
Split it into rectangles and add the areas, or take the big enclosing rectangle and subtract the missing corner.
