Right Trapezoid Area Calculator
Calculate the area of a right trapezoid using multiple methods
Calculate Right Trapezoid Area
The longer parallel side
The shorter parallel side
The perpendicular distance between bases
Area Calculation Result
Enter the required values
Enter both bases and height to calculate the area
Example Calculations
Example 1: Direct Method
Given: Longer base (a) = 10 units, Shorter base (b) = 6 units, Height (h) = 4 units
Solution: A = (a + b) × h / 2 = (10 + 6) × 4 / 2 = 16 × 2 = 32 square units
Example 2: Slant Side Method
Given: Longer base (a) = 12 units, Shorter base (b) = 8 units, Slant side (d) = 5 units
Step 1: Calculate height: h = √(d² - (a - b)²) = √(25 - 16) = √9 = 3 units
Step 2: Calculate area: A = (12 + 8) × 3 / 2 = 30 square units
Example 3: Angle Method
Given: Longer base (a) = 10 units, Shorter base (b) = 6 units, Slant side (d) = 5 units, Acute angle = 53.13°
Step 1: Calculate height: h = sin(53.13°) × 5 = 0.8 × 5 = 4 units
Step 2: Calculate area: A = (10 + 6) × 4 / 2 = 32 square units
Area Formula
A = Area of the trapezoid
a = Longer base (parallel side)
b = Shorter base (parallel side)
h = Height (perpendicular distance)
Calculation Methods
Direct Method
When you know both bases and height directly
Pythagorean Method
h = √(d² - (a - b)²)
Use when you know bases and slant side
Trigonometric Method
h = sin(angle) × d
Use when you know angle and slant side
Right Trapezoid Properties
Two parallel sides (bases)
Exactly two right angles (90°)
One perpendicular side
Height equals perpendicular side
Area = (sum of bases) × height ÷ 2
Understanding Right Trapezoid Area Calculation
What is a Right Trapezoid?
A right trapezoid is a special type of quadrilateral with exactly one pair of parallel sides (bases) and exactly two right angles. One of the non-parallel sides is perpendicular to both bases, making calculations much simpler than for general trapezoids.
Area Formula Derivation
The area formula A = (a + b) × h / 2 comes from the general trapezoid area formula. It represents the area of a trapezoid as the average of the two parallel sides multiplied by the height.
When to Use Each Method
- •Direct Method: When height is known directly
- •Slant Side Method: When only slant side is known
- •Angle Method: When angle information is available
Mathematical Relationships
Height from Slant Side
h = √(d² - (a - b)²)
Uses Pythagorean theorem on the right triangle formed
Height from Acute Angle
h = sin(δ) × d
Uses trigonometry with acute angle δ
Height from Obtuse Angle
h = sin(γ - 90°) × d
Uses trigonometry with obtuse angle γ
Median (Midsegment)
m = (a + b) / 2
Line parallel to bases through the midpoint