Axial Symmetric Pentagon calculator and formula

This function calculates various parameters of an axisymmetric pentagon.

To calculate, enter the lengths a, b and c and the angle alpha (α). Then click on the 'Calculate' button.

Axisymmetric pentagon calculator

Input

Base a

Middle side b

Top side c

Angle α

Decimal places

Results

Middle angle β

Base angle γ

Diagonal d

Height h

Perimeter U

Area A

Formulas for the axisymmetric pentagon

Diagonal

\(\displaystyle d =\sqrt{2·c^2-2·c^2·cos(α)} \)

Height

\(\displaystyle h =\sqrt{b^2-\left(\frac{d}{2}-\frac{a}{2}\right)^2 } +\sqrt{c^2-\left(\frac{d}{2}\right)^2} \)

Angle Beta

\(\displaystyle β =acos\left(\frac{b^2+c^2-e^2-(\frac{a}{2})^2}{2·b·c} \right) \)

Angle Gamma

\(\displaystyle γ = \frac{540°-α-2·β}{2}\)

Perimeter

\(\displaystyle p = a+2·b+2·c\)

Area

\(\displaystyle A = \frac{1}{4}·\sqrt{(d+a)^2·(d-a+2·b)·(a-d+2·b)}\) \(\displaystyle +\frac{1}{2}·\sqrt{\frac{4·c^2-d^2}{4}}·d\)

Axial Symmetric Pentagon Calculator

Calculate an axial symmetric pentagon

Formulas for the axisymmetric pentagon

Diagonal

Height

Angle Beta

Angle Gamma

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