Trapezoid Square Footage Calculator: Sloped Areas, Hip Roofs, and Irregular Plots
A trapezoid is any four-sided shape with exactly one pair of parallel sides. In construction, trapezoids show up as hip roof sections, sloped garden terraces, angled room additions, lot boundaries that follow road curves, and the cross-section of retaining walls and earthworks. You need three measurements: the two parallel sides (Base A and Base B) and the perpendicular height between them. The slant height of the non-parallel sides does not count.
This calculator uses the standard trapezoid formula. Enter Base A, Base B, and the perpendicular height in any unit for instant square footage results.
Trapezoid Area Formula
Formula: Area = ½ × (Base A + Base B) × Height
The height must be the perpendicular distance between the two parallel bases. Draw a right angle from one base to the other to measure it. The slant length of the non-parallel sides does not affect area (though it matters for perimeter and material edge trim).
Example: A trapezoidal patio with a 20 ft rear edge, a 14 ft front edge, and a depth of 12 ft. Area = ½ × (20 + 14) × 12 = ½ × 34 × 12 = 204 sq ft. Order 204 sq ft of pavers plus 15% waste for the angled front cuts.
Trapezoid Applications in Construction
- Hip roof sections: Each triangular hip end transitions to a trapezoidal main section. Use ½(ridge + eave length) × rafter length for each face.
- Angled lot boundaries: A property with a road frontage of 60 ft, a rear boundary of 80 ft, and a depth of 100 ft is a trapezoid: ½(60+80)×100 = 7,000 sq ft.
- Retaining wall face: A wall that is 8 ft tall at one end and 4 ft tall at the other, spanning 24 ft of run: ½(8+4)×24 = 144 sq ft of concrete block or stone facing.
- Tiered garden terrace: Each level has a different front and rear edge length, making each tier a trapezoid.
- Cathedral (vaulted) wall: A wall that is 8 ft tall on one side and 14 ft tall at the peak. Use our calculator for the right-trapezoid area of siding or drywall needed.
Right Trapezoid: Cathedral Walls and Sloped Ceilings
A right trapezoid has one vertical (90°) side and one sloped side. This shape represents a wall under a sloped ceiling or a vaulted room end wall. To find the drywall or siding area: Area = ½ × (Short Height + Tall Height) × Width. For a wall that is 8 ft on the low side, 13 ft on the high side, and 18 ft wide: ½ × (8+13) × 18 = 189 sq ft of drywall or siding.
Trapezoid vs. Triangle Distinction
A common mistake is treating a trapezoidal plot as a triangle by ignoring the shorter parallel side. If the shorter base is even 5 ft, the error on a 100 ft deep lot is ½ × 5 × 100 = 250 sq ft, enough to misstate a lot's value by thousands of dollars. Always measure both parallel sides and use the full trapezoid formula.
Related tools: triangle calculator · polygon calculator · roof calculator · wall calculator
Trapezoidal Garden Beds and Patio Edges
Properties on curving streets often have front lawns and driveways that form trapezoids. If your property frontage is 55 ft at the street and 70 ft at the house foundation, with a 40 ft setback depth, the trapezoidal front lawn area is ½ × (55 + 70) × 40 = 2,500 sq ft. At a seed application rate of 4 lbs per 1,000 sq ft, you need 10 lbs of grass seed for this trapezoidal front lawn. For fertiliser at 5,000 sq ft coverage per bag: 2,500 / 5,000 = half a bag. Converting 2,500 sq ft to acres for a sprinkler controller set in acres: 2,500 / 43,560 = 0.057 acres. That number helps you avoid over-watering or under-watering your front lawn zone.