Android app on Google Play

Quadrilateral

A quadrilateral is a shape of plane geometry with four straight sides and four vertices (corners). The side lengths and the angles of the vertices are not necessarily equal; neither do they need to have any specific values.

The sum of the four angle measures of a square is always 3600.

Categories

Quadrilaterals can be divided into the following categories:


Type and descriptionFormulas

Square
Square with right angles
All four sides of a square are
of equal length and all four
angle are 90° (right angles).

Area
A=a^2
Circumference
C=4*a
Diagonal length
d=sqrt{2}*a
Area of the inscribed circle
A=a*frac{pi}{4}
Area of the circumscribed circle
A=a*frac{pi}{2}
Rhombus
Rhombus with diagonals and angle alpha
All four side of a Rhombus are
of equal length. The angles are
pairwise equal but not
necessarily 90°.

Area
A=frac{1}{2}*d_1*d_2
A=sin(alpha)*a^2
A=2*a*r
Circumference
C=4*a
Rectangle
Drawing of a rectangle
The sides of a rectangle are
pairwise of equal length,and all
four angles are 90° (right angles).

Area
A=h*b
Circumference
C=2*(h+b)
Diagonal length
d=sqrt{h^2+b^2}
Parallelogram
Drawing of a parallelogram
The sides of a parallelogram
are pairwise of equal length and
parallel. The angles are pairwise
equal but not necessarily 90°.


Area
A=b*h
A=a*b*sin(theta)
Circumference
C=2*a+2*b
Trapezoid
Example of a trapezoid with diagonals, angles and side lengths
Two sides of a trapezoid are
parallel.

Height
h=b*sin(C)=d*sin(D)

or

h=frac{2}{a-c}*sqrt{s*(s-a+c)*(s-b)*(s-d)}

where s=frac{a+b-c+d}{2} and a>c
Area
A=frac{1}{2}*(a+c)*h
Circumference
C=a+b+c+d
C=a+b+h*(frac{1}{sin(A)}+frac{1}{sin(B)})
Diagonal length
d_1=sqrt{a^2+b^2-2*a*b*cos(B)}
d_1=sqrt{c^2+d^2-2*c*d*cos(D)}
d_2=sqrt{a^2+d^2-2*a*d*cos(A)}
d_2=sqrt{b^2+c^2-2*b*c*cos(C)}
Trapezium
Drawing of a trapezium
A trapezium has not necessarily
parallel sides or right angles.

The area can be determined
by dividing the trapezium
into two triangles and then
calculate the area of each
of them with the formula:
A_{triangle}=frac{1}{2}*h*g

The circumference is the
sum of all side lengths.

Quadrilaterals fitting into more than one category.

The different categories of quadrilaterals do not exclude each other.

A square is also a rectangle, for instance. In everyday language, however, the word rectangle is normally referred to as a quadrilateral having four right angles but only sides with pairwise equal length.

The quadrilateral is abut it is also a
Squarerectangle, Rhombus, Parallelogram,
Trapezoid, Trapezium
RhombusParallelogram, Trapezoid, Trapezium
rectangleParallelogram, Trapezoid, Trapezium
ParallelogramTrapezoid, Trapezium
TrapezoidTrapezium