How trapezoid area works (formula, examples, FAQs)

A trapezoid (also called a trapezium in some countries) is a four‑sided shape with one pair of parallel sides. Those parallel sides are called the bases. The distance between the bases (measured at a right angle) is the height. The trapezoid area formula is one of the most useful “real life geometry” tools because trapezoids show up everywhere: roof lines, ramps, bridges, garden beds, tabletops, floor plans, packaging, and even graphs (think of trapezoids under a curve).

This calculator is built for speed and sanity: enter the two base lengths and the height, pick your unit, and you’ll get the area instantly. It also gives a step‑by‑step breakdown you can screenshot and share (perfect for homework checks, DIY projects, and quick estimates).

Trapezoid Area Formula

The core formula is:

Area = ((Base 1 + Base 2) ÷ 2) × Height

In symbols, you’ll often see:

A = ((a + b) / 2) · h

• a = length of the first base (one parallel side)
• b = length of the second base (the other parallel side)
• h = height (the perpendicular distance between the bases)

Why the formula works (intuitive explanation)

The trapezoid area formula is basically “average base × height.” Here’s the intuition: if you take the two bases, a and b, and average them, you get the length of a “middle” segment that represents the typical width of the shape as you move from one base to the other. Multiply that average width by the height and you get the total area.

Another popular way to see it: copy the trapezoid, flip the copy, and fit the two together. Two identical trapezoids can form a parallelogram whose base is (a + b) and whose height is h. Since a parallelogram’s area is base × height, the combined area is (a + b) × h. One trapezoid is half of that, so:

A = ((a + b) × h) ÷ 2

Step‑by‑step: How to use this calculator

1. Enter Base 1: one of the parallel sides.
2. Enter Base 2: the other parallel side.
3. Enter Height: the straight perpendicular distance between the bases (not the slanted side).
4. Select units: cm, m, in, ft, etc. (units don’t change the math—just the label on the answer).
5. Press Calculate Area. You’ll see the numeric result, the formula substitution, and a clean “shareable” breakdown.

Common mistakes (and how to avoid them)

• Using a slanted side as the height: The height must be measured at a right angle to the bases. If you only know the slanted side, you may need extra info (like an angle or the base difference) to find the true height.
• Mixing units: If Base 1 is in inches and Base 2 is in feet, convert first. The calculator assumes both bases and the height are in the same unit.
• Swapping base vs. leg: Bases are the parallel sides. The non‑parallel sides are legs. Only the bases go into (a + b).
• Forgetting the ÷2: The trapezoid formula has an average or a half—don’t accidentally compute (a + b) × h (that’s double the trapezoid’s area).

Worked examples

Example 1 (simple numbers)

Base 1 = 10 cm, Base 2 = 6 cm, Height = 4 cm.

• Add bases: 10 + 6 = 16
• Average bases: 16 ÷ 2 = 8
• Multiply by height: 8 × 4 = 32

Area = 32 cm²

Example 2 (decimal inputs)

Base 1 = 3.5 m, Base 2 = 7.2 m, Height = 2.0 m.

• Add bases: 3.5 + 7.2 = 10.7
• Average bases: 10.7 ÷ 2 = 5.35
• Multiply by height: 5.35 × 2.0 = 10.7

Area = 10.7 m²

Example 3 (DIY / construction vibe)

You’re building a trapezoid‑shaped garden bed. The top base is 8 ft, the bottom base is 12 ft, and the height is 5 ft.

Area = ((8 + 12) ÷ 2) × 5 = (20 ÷ 2) × 5 = 10 × 5 = 50 ft². That’s the surface area you’d cover with soil, mulch, or landscape fabric.

What if you have legs instead of height?

Sometimes you know the non‑parallel sides (legs) instead of the height—especially in word problems. To use the trapezoid formula, you must still find the perpendicular height. If the trapezoid is right (one leg is perpendicular), that leg is the height. If it’s an isosceles trapezoid (legs equal), you can drop perpendiculars and use the Pythagorean theorem once you know the base difference.

Quick idea: in an isosceles trapezoid, each “side triangle” has a horizontal run of (|a − b| ÷ 2). If leg length is ℓ, then:

h = √(ℓ² − (|a − b| / 2)²)

Once you have h, plug it back into A = ((a + b) / 2) · h.

Units, conversions, and real‑world interpretation

Area units are always “squared” because area is two‑dimensional:

• cm → cm²
• m → m²
• in → in²
• ft → ft²

If you’re converting to bigger units (like ft² to yd²), do the conversion after you compute area. A quick reminder: 1 yd = 3 ft so 1 yd² = 9 ft². That means you divide by 9 to convert from ft² to yd².

Where trapezoids show up (use cases)

• Architecture: roof sections, gables, sloped ceilings, window panes.
• Construction: ramps, driveway flares, retaining wall faces, concrete forms.
• DIY projects: tabletops, shelves, garden beds, custom signage.
• Math & school: geometry homework, coordinate geometry, composite shapes.
• Engineering: trapezoidal channels, cross‑sections, simplified area estimates.

FAQ (Frequently Asked Questions)

• Do I need Base 1 to be the longer base?

  No. The formula is symmetric: swapping the bases doesn’t change the result. Enter them in any order.

• What if my trapezoid is rotated?

  Rotation doesn’t matter. As long as you identify the two parallel sides and the perpendicular height, the formula works.

• What if I only know the perimeter?

  Perimeter alone isn’t enough to determine area. You need a height (or more information like angles/coordinates).

• What’s the difference between a trapezoid and a parallelogram?

  A parallelogram has two pairs of parallel sides. A trapezoid has exactly one pair of parallel sides (in the common U.S. definition).

• Can the trapezoid area formula be used for graphs (trapezoid rule)?

  The “trapezoid rule” in calculus uses the same area idea, approximating curved areas by adding up many small trapezoids.

• Why does my answer look “too big”?

  Check the height: it must be perpendicular. Also confirm you didn’t accidentally input different units (e.g., inches and feet).

• Does this calculator store my data?

  No. Your inputs stay in your browser. If you use “Save Result,” it stores locally on your device (not on a server).

Pro tip for virality (shareable math)

If you’re a student, builder, or teacher: calculate a few examples, then screenshot the step‑by‑step breakdown. It’s one of the fastest ways to confirm an answer, explain your work, or send a clean “here’s the math” message in a group chat.

Want to combine shapes?

If your real-world shape is made of multiple parts, break it into rectangles, triangles, and trapezoids, compute each area, and add them together. For cut-outs (holes), subtract those areas.

• Use the Triangle Area tool for triangular pieces.
• Use the Rectangle Calculator for rectangles.
• Use the Polygon Area tool for many-sided regions.

Remember: keep units consistent across all parts before adding or subtracting.