Area of a Trapezium Calculator

Enter both parallel sides and the perpendicular height — get area and step-by-step working instantly.

Unit:
Parallel Side a
cm
Parallel Side b
cm
Height (h) — perpendicular
cm

Optional — add legs for perimeter

Leg c
cm
Leg d
cm

Enter both parallel sides and height to calculate area.

Diagram

Trapezium Area Formulas

Primary Formula

A = ½ × (a + b) × h

a, b are parallel sides; h is perpendicular height.

Using Midsegment

A = m × h

m = (a + b) / 2 is the average of the parallel sides.

Height from Area

h = 2A ÷ (a + b)

Rearrange the primary formula to solve for height.

Midsegment

m = (a + b) ÷ 2

The midsegment is parallel to both bases and equals their average.

What Is a Trapezium?

A trapezium (British English) is a quadrilateral with exactly one pair of parallel sides. The parallel sides are called the bases (a and b), and the non-parallel sides are called the legs. The perpendicular distance between the two bases is the height (h).

The area formula A = ½ × (a + b) × h can be understood intuitively: the trapezium has the same area as a rectangle whose width is the average of the two parallel sides (the midsegment) and whose height equals the trapezium's height.

½(a+b)×h
Primary formula — average the parallel sides then multiply by height
m = (a+b)/2
Midsegment — connects midpoints of the two legs
P = a+b+c+d
Perimeter — sum of all four sides

How to Calculate the Area of a Trapezium

  1. 1

    Identify the two parallel sides (a and b)

    One parallel side is usually longer (the base) and the other shorter (the top). Label the longer one a and the shorter one b, or vice versa — the formula works either way.

  2. 2

    Measure the perpendicular height (h)

    The height is the shortest distance between the two parallel sides — always measured at a right angle to them, not along the slanted legs.

  3. 3

    Apply A = ½ × (a + b) × h

    Add the two parallel sides, multiply by height, then halve the result. The result is in square units.

Worked Example — Trapezium with parallel sides 12 cm and 8 cm, height 5 cm

Given: a = 12 cm, b = 8 cm, h = 5 cm
Formula: A = ½ × (a + b) × h
Step 1: a + b = 12 + 8 = 20 cm
Step 2: A = ½ × 20 × 5 = ½ × 100
Area: A = 50 cm²
Midsegment: m = (12 + 8) / 2 = 10 cm

Real-World Applications

🏗️

Architecture

Trapezoidal roof cross-sections and gable ends are calculated using this formula to estimate material needs.

🛣️

Civil Engineering

Road embankments, canal cross-sections, and retaining walls typically have trapezoidal profiles for stability.

🎨

Design

Perspective drawings in art and graphic design frequently use trapezoids to represent rectangles viewed at an angle.

🌿

Landscaping

Trapezoidal plots and sloped garden terraces are common in hilly areas where irregular land shapes must be measured accurately.

📐

Education

The trapezium is a key shape in class 8–10 geometry, and the trapezoidal rule is used in calculus for numerical integration.

Common Trapezium Measurements

Parallel Side a Parallel Side b Height Area
12 cm 8 cm 5 cm 50 cm²
20 cm 10 cm 8 cm 120 cm²
15 m 9 m 6 m 72 m²
100 m 60 m 30 m 2400 m²
30 cm 20 cm 15 cm 375 cm²

Frequently Asked Questions

What is the area formula for a trapezium?
A = ½ × (a + b) × h where a and b are the parallel sides and h is the perpendicular height. For parallel sides 12 cm and 8 cm with height 5 cm: A = ½ × 20 × 5 = 50 cm².
What is a trapezium (vs trapezoid)?
In British English, a trapezium has exactly one pair of parallel sides. In American English, this shape is called a trapezoid. This calculator follows the British convention.
How is the midsegment used in the area formula?
The midsegment m = (a + b) / 2 is the average of the two parallel sides. Area = m × h. Think of it as converting the trapezium into an equivalent rectangle with width m and height h — same area, simpler shape.
Can you calculate perimeter from parallel sides and height alone?
No — you also need the lengths of the two non-parallel legs (c and d). The height alone tells you the perpendicular distance but not how long the slanted sides are. Add the leg lengths in the optional fields above.
What if both parallel sides are equal?
If a = b, the shape becomes a parallelogram and the formula simplifies to A = a × h — the same as the parallelogram formula. The trapezium formula still gives the correct answer: A = ½ × (a + a) × h = a × h.

Related Area Calculators

Circle Semicircle Square Rectangle Parallelogram Rhombus Scalene Triangle Right Triangle Equilateral Triangle Isosceles Triangle Regular Hexagon Sector & Segment