Area and perimeter of a trapezium

A trapezium (trapezoid) is a parallelogram which has one pair of parallel edges.
The parallel edges are called bases, those not parallel are legs.
The diagonals neither halve one another nor are perpendicular to one another.
The height is the perpendicular distance between the bases.

trapezium

a, b, c, d	edge
d_1,2	diagonals
h	height
α, β, γ, δ	angle

Calculator

Select the units of measurement

Enter 4 values

edge

a =

edge

b =

edge

c =

edge

d =

height

h =

angle

α =

angle

β =

angle

γ =

angle

δ =

area

A =

perimeter

P =

Error

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Calculation procedure

Formulas

trapezium

area

$$ A = \frac{(a + c) \cdot h}{2} $$

perimeter

$$ P = a + b + c + d $$

diagonal

$$ \begin{aligned} d_1 &= \sqrt{a^2 + b^2 - 2 \cdot a b \cos\beta} \\ \\ d_2 &= \sqrt{a^2 + d^2 - 2 \cdot a d \cos\alpha} \end{aligned} $$

angle

$$ \begin{aligned} \gamma &= 180^\circ - \beta \\ \\ \delta &= 180^\circ - \alpha \end{aligned} $$

height

$$ h = d \cdot\sin\alpha = b \cdot\sin\beta $$

Area and perimeter of a trapezium

trapezium

Calculator

Select the units of measurement

Enter 4 values

edge

edge

edge

edge

height

angle

angle

angle

angle

area

perimeter

Error

Calculation procedure

Formulas

trapezium

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