Area of Trapezoids Practice Problems & Conceptual Mastery
If you duplicate any trapezoid and flip it upside down next to the original, the two trapezoids form a single parallelogram whose base is the sum of the two parallel bases (a + b) and whose height is h. Since the trapezoid is half of this parallelogram, its area is Area = ½ × (a + b) × h.
📝 Worked Step-by-Step Example
1. Add bases: 5 + 11 = 16. 2. Halve the sum: 16 ÷ 2 = 8. 3. Multiply by height: 8 × 4 = 32 m².
🧠 Core Problem-Solving Strategies
1. The Average Base Rule
Area = (average of the bases) × height = [(a + b) ÷ 2] × h.
2. Add the Bases First
Always resolve the parentheses (a + b) before multiplying by height or halving.
3. Perpendicular Height Only
Never use the slanted legs of the trapezoid as the height. Always use the perpendicular vertical distance.
📖 Key Mathematical Terms & Vocabulary
Parallel Bases (a and b)
Altitude / Height (h)
❓ Frequently Asked Questions
What makes a quadrilateral a trapezoid?
In American geometry, a trapezoid is a quadrilateral with at least one pair of parallel sides (called bases).
Can the parallel bases be vertical?
Yes! If the trapezoid is turned sideways, the parallel bases run vertically, and the perpendicular height is measured horizontally between them.
What is an isosceles trapezoid?
An isosceles trapezoid is one where the two non-parallel slanted legs are equal in length.
Continue Learning & Practicing Area of Trapezoids
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