Trapezoid

Trapezoidal Mulch Calculator

A 9 × 5 ft fence-edge trapezoid 4 ft deep — the bed that runs from a 90° corner toward an angled property line — comes out to exactly 28 sq ft of mulch coverage, or 7 cu ft at the standard 3-inch depth. This is the most common trapezoid shape in residential landscaping, and almost nobody measures it correctly the first time. The math: ½ × (parallel side A + parallel side B) × perpendicular height.

A trapezoidal planting bed running along a white picket fence, narrower at one end and wider at the other, freshly mulched with coneflowers, lavender, and sage. — Photograph for MulchCalc.

The worksheet

Do the
math here.

Enter dimensions in the units you measured in. The page does the converting — cubic feet, cubic yards, bag counts, and price — without sending your numbers anywhere.

Worked example: a fence-corner trapezoid

Reviewed by MulchCalc Editorial Team · Updated June 2026 · Sources 3 cited

The key step most homeowners get wrong is the height. The height is the perpendicular distance between the two parallel sides — not the slant side. If your tape runs along the angled edge, you've measured the slant and the area will come out 10–20% too high.

Deriving the formula from the example

The trapezoid formula is just the average-width-times-height shortcut: Area = ½ × (a + b) × h, where a and b are the parallel sides and h is the perpendicular gap between them. The ½ is doing the averaging.

Reading it back: a 9 × 5 ft trapezoid is equivalent in area to a 7 ft wide rectangle of the same height. That's why the result (28 sq ft) is exactly what you'd get for 7 × 4 — the average of 9 and 5 is 7.

Where trapezoids show up on real lots

Driveway transitions. A planting strip runs along the driveway and tapers to meet a sidewalk or fence at an angle.
Property-line beds. Many lots have angled rear boundaries; foundation beds become trapezoidal where they wrap around the angle.
Slope tapers. Hillside beds narrow as elevation drops, creating a natural trapezoid along the contour line.
Corner-cut HOA strips. Curb-side beds where the road bends at an intersection — almost always trapezoidal.

Quick-reference area table

Side A (ft)	Side B (ft)	Height (ft)	Area (sq ft)	Cu ft at 3 in
6	4	3	15	3.75
8	5	4	26	6.5
9	5	4	28	7.0
10	6	5	40	10.0
12	8	6	60	15.0
15	10	8	100	25.0

When to split into simpler shapes

Sides not parallel within 15°. Split into a rectangle plus 1 or 2 triangles, sum the areas. The irregular mulch calculator does this automatically.
More than four sides. Any pentagonal or hexagonal bed: decompose into triangles using the diagonal method.
Curved parallel side. Approximate the curve with three straight segments, treat as three small trapezoids end-to-end.
Heavily sloped ground. Use the slant length as your perpendicular height only when slope is under 5%; above that, project to horizontal.

Reading list

Related guides

Reader Letters

Frequently asked questions

How do I find the height of a trapezoid?+

Drop a tape perpendicular from one parallel side to the other. That perpendicular distance is the height — not the slant edge. A carpenter's square or a string line at 90° to one parallel side gives you the right reference line in under a minute.

What if my parallel sides aren't actually parallel?+

Measure both 'parallel' sides anyway and treat them as parallel. As long as they're within 15° of true parallel, the formula gives a workable estimate (within 5%). Beyond 15°, split into a triangle plus a rectangle and use the irregular calculator.

How much mulch for a typical driveway trapezoid?+

A 9 × 5 ft trapezoid 4 ft deep is 28 sq ft. At 3-inch depth: 7 cu ft = 4 bags of 2 cu ft, about $18 at 2026 prices. Add 10% for settling and you still land on 4 bags.

Can I use this for an isosceles trapezoid?+

Yes — the formula works for any trapezoid regardless of symmetry. The two slant sides being equal doesn't change anything; only the parallel sides and the perpendicular height feed the math.

What about a 4-sided bed with no parallel sides?+

That's a general quadrilateral, not a trapezoid. Split it with a diagonal into two triangles, calculate each with ½ × base × height, and add. The triangular mulch calculator runs both halves for you.

Best edging for trapezoidal beds?+

Steel edging cuts cleanly along straight angles; flexible plastic works better on curved sides. Skip rigid pavers on angled runs — they create visible gaps at every joint. Penn State's bulletin lists steel as the longest-lasting option at 12–15 years.

Does slope affect the trapezoid area?+

Yes. If the bed sits on a hillside steeper than 5%, the tape-measured length over-estimates the horizontal area. Convert by multiplying by cos(slope angle), or measure the horizontal projection directly with a level tape.

How do I lay out a trapezoid on bare soil?+

Stake the four corners, run a string between each pair, then spray-paint along the strings. Verify perpendicular height with a carpenter's square at any point along the shorter parallel side before you start digging.

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