Polygon is a closed plane figure made up of several line segments that are joined together. The sides do not cross each other. Exactly two sides meet at every vertex.
Types of Polygons
Regular – all angles are equal and all sides are the same length. Regular polygons are both equiangular and equilateral. Equiangular – all angles are equal. Equilateral – all sides are the same length.
Polygon Formulas (N = number of sides , S = length from center to a corner)
Area of regular polygon
= (1/2) N sin(360°/N) S 2
Sum of interior angles of a polygon = (N – 2) x 180°
The number of diagonals in a polygon = 1/2 N (N-3)
The number of triangles (when you draw all the diagonals from one vertex) in a polygon = (N – 2)
Polygon Parts Side – one of the line segments that make up the polygon.
Vertex – point where two sides meet. Two or more of these points are called vertices.
Diagonal – a line connecting two vertices that isn’t a side. Interior Angle – Angle formed by two adjacent sides inside the polygon.
Exterior Angle – Angle formed by two adjacent sides outside the polygon.
Special Polygons Special Quadrilaterals – square, rhombus, parallelogram, rectangle, and the trapezoid.
Special Triangles – right, equilateral, isosceles, scalene, acute, obtuse.
Polygon Names
Sides Name N
3. Triangle
4. Quadrilateral
5. Pentagon
6. Hexagon
7. Heptagon
8. Octagon
10. Decagon
Area Formulas:
Square = a ²
Rectangle = a * b
Parallelogram = b * h
Trapezoid = h / 2 (b 1 + b 2 )
Circle = π* r 2
Ellipse = π* r 1* r 2
Triangle = ½ b * h
Equilateral triangle = √3/4 a²
Triangle given two sides and the opposite angle = (1/2) * a * b * sin C Triangle given a,b,c
√s * (s-a) * (s-b) * (s-c)
where s=(a + b + c) / 2
Volume Formulas:
Cube = a ³
Triangular prism = ( 1 / 2) l b h. Rectangular prism = l b h
Pyramid = (1/3) b h
Cone = (1/3) b
—–:h = 1/3 π r ²h
Sphere = (4/3) πr ³
Ellipsoid = (4/3) π r 1 r 2 r³ Cylinder = πr²h
Surface Area Formulas:
Cube = 6 a²
Prism = 2ab + 2bc + 2ac
Sphere = 4 πr ²
Cylinder = 2 π r ²+ 2πrh
Perimeter Formulas :
Square = 4a
Rectangle = 2a + 2b
Triangle = a + b + c
Circle = 2πr
Circle = πd (where d is the diameter)