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Polygon(shapes) convex and concave

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Polygon Booklet

By; Summer Robles 


Regular Polygons;

An equilateral shape of figure

*All sides and angles are exactly the same; equal in measure

closed in figure with 3 or more sides

  (no gaps/overlaps)    (no curves)

In an equilateral triangle each angle is 60° all sides are equal

An acute* triangle has 3 acute angles

*acute mean an angle that its less that 90°

Scalene Triangle, with 3 uneven sides

Isosceles triangle, 2 sides are parallel and 2 angles are equal, 3rd side/angle is unequal

(a pair of equal sides and angles)

Obtuse triangle, one obtuse angle(greater that 90°), the rest of the angles are acute

Right triangle, 1 right triangle(90°), 2 acute angles (89° or less)

The total degree for triangles is 180°, exterior angle is 60°

Parallelogram, two pairs of parallel sides and opposite sides are equal
Two long sides of the same length and two short sides of the same length. Opposite angles are also equal

Square is equilateral and all angles are right angles (90°)


- A 4-sided figure, opposite sides are parallel (||) and opposite angles are equal and add up to 360°

Parallel (||) sides are are identical in measure

Congruent(≅) means that they are equal

Rectangle, opposite sides are parallel/congruent, all angles are 90°

A Kite has two pairs of adjacent sides of the same length

*Adjacent means next to or adjoining something else


              (4 sides - 360°)

Exterior angle is 45°

Trapezoid has exactly one pair of parallel sides

Rhombus, equilateral parallelogram with 4 equal sides and all angles (90°)

Interior angle - 108°
Exterior angle - 36°

A six sided shape has a total degree of 720

A five sided shape's, total degree is 540

Interior angle - 120°
Exterior angle - 30°
Interior angle - 128.5°
Exterior angle - 25.7°

A seven sided shape has a total degree of 900

The total degree of a eight sided shape is 1,080

Interior angle - 135°
Exterior angle - 22.5°

The total degree of a nine sided shape is 1,260

A ten sided shape, has the total degree of 1,440

Interior angle - 144°
Exterior angle - 18°
Interior angle - 140°
Exterior angle - 20°

Total degree for a 12 sided polygon is 1,800

Interior angle - 150°
Exterior angle - 15°

Total degree of an eleven sided shape is 1,620

Interior angle - 147.2°
Exterior angle - 16.36°

-Concave have at least 1 angle greater than 180 degrees, it caves in


-Convex, all angles are less that 180 degrees

Convex        Vs.       Concave

All regular polygons are convex

5 sided polygon is a pentagon

Regular     Vs     Irregular