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xGeometry

Isosceles Triangle

Base
$$b$$
Oblique Side
$$S$$
Height
$$h$$
$$2p = b + S \times 2$$
Perimeter
$$b = 2p - S \times 2$$
$$S = \frac{2p - b}{2}$$
$$A = \frac{b \times h}{2}$$
Area
$$b = \frac{A \times 2}{h}$$
$$h = \frac{A \times 2}{b}$$
$$S = \sqrt{ {h}^2 + {\left(\dfrac{b}{2}\right)}^2 }$$
Oblique Side (Pythagoras' theorem)
$$h = \sqrt{ {S}^2 - {\left(\dfrac{b}{2}\right)}^2 }$$
$$b = \sqrt{ {S}^2 - {h}^2 } \times 2$$

Definition

An isosceles triangle is a triangle with two congruent sides

Properties

  1. Two congruent sides
  2. Base angles are congruent
  3. All the  Generic Triangle formulas are valid
  4. The height relative to the base divides the shape in two congruent right triangles. For these are valid the  Right Triangle formulas
Isosceles Triangle
Isosceles Triangle Formulas
Data Formula
Perimeter 2p = b + S × 2
Area A = (b × h) / 2
Oblique Side S = √[ h2 + (b / 2)2 ]
Base b = (A × 2) / h
Height h = (A × 2) / b
Base b = 2p - S × 2
Side S = (2p - b) / 2
Height h = √[ S2 + (b / 2)2 ]
Base b = √( S2 - h2 ) × 2