Right Trapezoid Formulas and Geometric Properties
In a right trapezoid (or right-angled trapezium), the perpendicular distance between both parallel bases is exactly equal to the length of the perpendicular side.
1. Area Formula
The area uses the standard formula since the perpendicular side is the height:
Area = ½ × (a + b) × h
2. Slant Leg via Pythagorean Theorem
By dropping an altitude from the end of the shorter base to the longer base, a right triangle is formed with hypotenuse $c$, vertical leg $h$, and base difference $|a - b|$:
c = √(h² + (a - b)²)
h = √(c² - (a - b)²) (requires c > |a - b|)
h = √(c² - (a - b)²) (requires c > |a - b|)
3. Perimeter
Perimeter = a + b + h + c