Description and formulas for the calculation of trapezoids
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
\(a\) Side length a
\(b\) Side length b
\(c\) Side length c
\(d\) Side length d
\(e\) Diagonal e
\(f\) Diagonal f
\(h\) Height
\(m\) Midsegment
\(A\) Area
\(P\) Perimeter
\(α\) Angle Alpha
\(β\) Angle Beta
\(γ\) Angle Gamma
\(δ\) Angle Delta
\(\displaystyle a = (A · 2) / h -c\)
\(a = m · 2 -c\)
\(\displaystyle b =h / sin(β)\)
\(b = h / sin(γ)\)
\(\displaystyle c = (A · 2 / h) - a\)
\(c = m · 2 - a\)
\(\displaystyle d = h / sin(α)\)
\(d = h / sin(δ)\)
\(\displaystyle e = \sqrt{a^2 + b^2 - 2 · a · b · cos(β)}\)
\(\displaystyle f = \sqrt{a^2 + d^2 - 2 · a · d · cos(α)}\)
\(\displaystyle h = (2 · a) / (a + c)\)
\(h = b · sin(β)\)
\(\displaystyle m = (a + c) / 2\)
\(m = A / h\)
\(\displaystyle A = (a + c) / 2 · h\)
\(A = m · h\)
\(\displaystyle P = a + b + c+ d\)
\(\displaystyle α = asin(h / d)\)
\(\displaystyle α = 180 - δ\)
\(\displaystyle β = asin(h / b)\)
\(\displaystyle β = 180 - γ\)
\(\displaystyle γ = 180 - β\)
\(\displaystyle δ = 180 - α\)