Geometric Formulas for 2D Polygons

Vocabulary practice flashcards covering perimeter, area, height, and side formulas for standard geometric shapes and polygons.

Rectangle (Rechteck)

A quadrilateral with opposite equal sides where the perimeter is $u = (a + b) \times 2$, the area is $A = a \times b$, and the diagonal is d = \root{}{a^2 + b^2}.

Square (Quadrat)

A regular four-sided polygon where all sides equal $a$, the perimeter is $u = 4a$, the area is $A = a^2$, and the diagonal is d = \root{}{a^2 + a^2} = a\root{}{2}.

General Triangle (Allgemeines Dreieck)

A three-sided polygon with perimeter $u = a + b + c$ and area calculated by $A = \frac{a \times h_a}{2} = \frac{b \times h_b}{2} = \frac{c \times h_c}{2}$.

Equilateral Triangle (Gleichseitiges Dreieck)

A triangle where all three sides are equal ($a = b = c$), the perimeter is $u = 3a$, the height is h = \root{}{a^2 - \frac{a^2}{4}}, and the area is $A = \frac{a \times h}{2}$.

Isosceles Triangle (Gleichschenkliges Dreieck)

A triangle with two equal sides ($a = b$), perimeter $u = 2a + c$, height to base h_c = \root{}{a^2 - \frac{c^2}{4}}, and area $A = \frac{c \times h_c}{2}$.

Right-angled Triangle (Rechtwinkliges Dreieck)

A triangle with a right angle ($\nu = 90^{\circ}$), perimeter $u = a + b + c$, area $A = \frac{a \times b}{2} = \frac{c \times h_c}{2}$, and hypotenuse given by the Pythagorean theorem as c = \root{}{a^2 + b^2}.

General Parallelogram (Allgemeines Parallelogramm)

A quadrilateral with pairwise parallel opposite sides, perimeter $u = (a + b) \times 2$, and area $A = a \times h_a = b \times h_b$.

Rhombus (Raute)

An equilateral parallelogram with perimeter $u = 4a$, area $A = a \times h = \frac{e \times f}{2}$, and side length a = \root{}{\frac{e^2}{4} + \frac{f^2}{4}}, where $e$ and $f$ are the diagonals.

General Trapezoid (Allgemeines Trapez)

A quadrilateral with one pair of parallel bases ($a$ and $c$), perimeter $u = a + b + c + d$, and area $A = \frac{(a + c) \times h}{2}$.

Right-angled Trapezoid (Rechtwinkliges Trapez)

A trapezoid with right angles, perimeter $u = a + b + c + d$, area $A = \frac{(a + c) \times h}{2}$, horizontal offset $x = a - c$, height h = \root{}{b^2 - x^2}, and slant leg b = \root{}{h^2 + x^2}.

Isosceles Trapezoid (Gleichschenkliges Trapez)

A trapezoid with two equal non-parallel legs ($b = d$), perimeter $u = a + 2b + c$, area $A = \frac{(a + c) \times h}{2}$, and height h = \root{}{b^2 - \frac{(a - c)^2}{4}}.

Kite (Deltoid / Drachenviereck)

A quadrilateral with two pairs of equal adjacent sides, perimeter $u = (a + b) \times 2$, area $A = \frac{e \times f}{2}$, and diagonal segment x = \root{}{b^2 - \frac{f^2}{4}}.