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xGeometry

Isosceles Trapezoid

Longer Base
$$B$$
Shorter Base
$$b$$
Height
$$h$$
Oblique Side
$$S$$
Oblique side Projection
$$p_{1}$$
Diagonal
$$d$$
$$2p = B + b + 2S$$
Perimeter
$$A = \frac{\left(B + b \right) \times h}{2}$$
Area
$$B + b = \frac{2A}{h}$$
Sum of bases
$$h = \frac{2A}{B + b}$$
Height
$$B + b = 2p - 2S$$
Sum of bases
$$S = \frac{2p - B - b}{2}$$
Oblique Side
$$p_{1} = \frac{ B - b }{2}$$
Oblique side Projection
$$B - b = 2 \times p_{1}$$
Difference of bases
$$B = b + 2p_{1}$$
Longer Base
$$b = B - 2p_{1}$$
Shorter Base
Right Tr. delimited by height - oblique side
$$S = \sqrt{ {p_{1}}^2 + {h}^2 }$$
Side (Pythagoras' theorem)
$$h = \sqrt{ {S}^2 - {p_{1}}^2 }$$
Height
$$p_{1} = \sqrt{ {S}^2 - {h}^2 }$$
Oblique side Projection
Definition
An isosceles trapezoid is a trapezoid with oblique sides congruent
Properties
  1. The oblique sides are congruent
  2. The angles adjacent to their respective bases are congruent
  3. Diagonals are congruent
  4. All the  Generic Trapezoid formulas are valid