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# 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 Isosceles Trapezoid Formulas
Data Formula
Perimeter 2p = B + b + 2 × S
Area A = [(B + b) × h] / 2
Height h = (2 × A) / (B + b)
Oblique Side S = (2p - B - b) / 2
Oblique side Projection p1 = (B - b) / 2
Sum of bases B + b = (2 × A) / h
Sum of bases B + b = 2p - 2 × S