RedCrab Math Tutorial

# Trapezoid Calculation

A trapezoid is a quadrangular geometric shape with the following characteristics
• A trapezoids have one pair of parallel sides, which are the bases of the trapezoid

• The opposite sides are different in length

• The midsegment m of a trapezoid is parallel to each base. Its measure is one half of the sum of the measures of the bases

• The Figure above shows an isosceles trapezoid. The sides are also congruent. As seen in the figure, an isosceles trapezoid has two pairs of congruent angles, the diagonals are congruent, and it has one line of symmetry

## Trapezoid Properties

Eigenschaften die berechnet werden können
• Length

• Length

• Length

• Length

• Diagonal

• Diagonal

• Height

• Midsegment

• Area

• Perimeter

• Angle Alpha

• Angle Beta

• Angle Gamma

• Angle Delta

a

b

c

d

e

f

h

m

A

P

α

β

γ

δ

## Trapezoid Formulas

• Length
a a = (A · 2) / h -c a = m · 2 -c
• Length
b b = h / sin(β) b = h / sin(γ)
• Length
c c = (A · 2 / h) - a c = m · 2 - a
• Length
d d = h / sin(α) d = h / sin(δ)
• Diagonal
e e = √a² + b² - 2 · a · b · cos(β)
• Diagonal
f f = √a² + d² - 2 · a · d · cos(α)
• Height
h h = (2 · a) / (a + c) h = b · sin(β)
• Midsegment
m m = (a + c) / 2 m = A / h
• Area
A A = (a + c) / 2 · h A = m · h
• Perimeter
P P = a + b + c+ d
• Angle Alpha
α α = cos(h / d)
• Angle Beta
β β = cos(h / b)
• Angle Gamma
γ γ = cos(h / b)
• Angle Delta
δ δ = cos(h /d)

Example with RedCrab Calculator
• For calculation, the object t of the class Trapez is used