Trapezoid Calculator — Area, Perimeter & Median
Calculate the area, perimeter, and median of a trapezoid with step-by-step explanation. Learn A = ½(b₁+b₂)h and explore special cases. For related tools, see our area calculator.
Table of Contents
Calculate Trapezoid Properties
Enter bases and height. Optionally enter leg lengths for perimeter. Click Calculate.
Trapezoid – Complete Explanation
A trapezoid (UK: trapezium) has one pair of parallel sides called bases. The perpendicular distance between bases is the height.
Trapezoid Formulas
A = ½(b₁ + b₂)h P = b₁ + b₂ + leg₁ + leg₂ m = (b₁ + b₂) / 2
1. What Is a Trapezoid?
A quadrilateral with at least one pair of parallel sides. Height is perpendicular to bases.
2. Area of a Trapezoid
A = ½(b₁ + b₂) × h
Average the bases, then multiply by height.
3. Perimeter of a Trapezoid
P = b₁ + b₂ + leg₁ + leg₂
4. Median (Midsegment)
m = (b₁ + b₂) / 2
Connects midpoints of legs; parallel to both bases.
5. Step-by-Step Examples
Example 1: b₁=10, b₂=16, h=6
A = ½(26)×6 = 78 | m = 13 | P = 40 (if legs = 7,7)
Example 2: Right trapezoid b₁=6, b₂=10, h=4
A = ½(16)×4 = 32 | m = 8
6. More Trapezoid Examples
b₁=5,b₂=15,h=4: A=40, m=10
b₁=3,b₂=9,h=10: A=60, m=6
b₁=b₂=7,h=6: A=42, m=7 (parallelogram!)
b₁=0,b₂=12,h=5: A=30, m=6 (triangle!)
7. Isosceles Trapezoid
Equal legs, equal base angles, equal diagonals.
8. Right Trapezoid
Two right angles; one leg equals height.
9. Common Mistakes
- Forgetting the ½ in area formula.
- Using slant height instead of perpendicular height.
- Confusing median with height.
- Assuming legs are equal.
- Using non-parallel sides as bases.
10. Real-World Applications
- Architecture: Trapezoidal windows and trusses.
- Engineering: Trapezoidal channels.
- Land Surveying: Trapezoidal rule for area.
- Furniture: Trapezoidal tabletops.
- Calculus: Trapezoidal rule for integration.
11. Practice Problems
P1: b₁=12,b₂=18,h=8 → A=120, m=15
P2: Isosceles: b₁=10,b₂=20,legs=13 → h=12
P3: Right: b₁=4,b₂=10,h=6 → A=42, m=7
P4: A=72, b₁=8, b₂=16 → h=6
12. Tips for Mastery
- Remember "average of bases × height."
- Median simplifies area to A = m × h.
- Isosceles: use Pythagorean theorem for height.
- Formulas work when b₁=b₂ (parallelogram) or b₁=0 (triangle).
13. Final Thoughts
The trapezoid area formula gracefully handles everything from rectangles to triangles. Master it thoroughly.
14. Frequently Asked Questions
A = ½(b₁ + b₂) × h. Average the bases, multiply by height.
m = (b₁ + b₂)/2. The segment connecting the midpoints of the legs.
P = b₁ + b₂ + leg₁ + leg₂. Sum of all four sides.
Equal legs, equal base angles, equal diagonals.
Two right angles; one leg equals the height.
The trapezoid becomes a parallelogram. A = b × h.
The trapezoid becomes a triangle. A = ½ × b₂ × h.
Explore Math Topics
Continue your learning journey with our other math guides
Related Calculators
Explore these other geometry tools:
- 🔹 Area Calculator — Area of common shapes.
- 🔹 Perimeter Calculator — Distance around shapes.
- 🔹 Rectangle Calculator — Rectangle properties.
- 🔹 Square Calculator — Square properties.
- 🔹 Triangle Area Calculator — Triangle area.
- 🔹 Kite Area Calculator — Kite area.
Conclusion
The trapezoid area formula gracefully handles everything from rectangles to triangles. Master it thoroughly.
Readers who wish to continue practicing can explore the companion learning resource for guided exercises.