Area of a Trapezoid Calculator

Find the area of a trapezoid using A = ½ × (a + b) × h. Enter the two parallel bases and the height; add both leg lengths to also get the perimeter and shape type.

Quick Facts

Formula
A = ½ × (a + b) × h
a and b are the two parallel sides (bases); h is the perpendicular distance between them, not the length of a slanted leg.
Midsegment
(a + b) ÷ 2
The segment joining the midpoints of the two legs is parallel to the bases and equals their average length.

Your Results

Calculated
Area
-
½ × (a + b) × h
Perimeter
-
Sum of all four sides (needs both legs)
Midsegment (median)
-
(a + b) ÷ 2, average of the bases
Shape type
-
Based on leg lengths

Ready

Enter both bases and the height, then press Calculate.

Formula and method for Area of a Trapezoid

Area of a Trapezoid:

A = ½ × (a + b) × h

a, b = parallel sides; h = height

A trapezoid is a four-sided shape (quadrilateral) with exactly one pair of parallel sides, called the bases. The area only depends on the two base lengths and the perpendicular distance between them — the height — never on the slanted leg lengths. That is why the formula averages the two bases, (a + b) / 2, and multiplies by the height: it treats the trapezoid as a rectangle whose width equals the average base.

How the calculation works

Enter the top base (a) and bottom base (b) in any consistent unit, then enter the height (h) — the straight-line perpendicular distance between the two bases, not the length of a slanted side. The calculator computes area as A = ½ × (a + b) × h. If you also know the two leg lengths, it adds their sum to the bases for the perimeter, and compares the legs to tell you whether the trapezoid is isosceles (equal legs) or scalene (unequal legs).

Common mistakes

  • Height vs. leg: the height must be measured perpendicular to the bases. A slanted leg is always longer than or equal to the height — using leg length in place of height overstates the area.
  • Units: area comes out in square units (ft², m², etc.). A trapezoid with bases in feet and a height in feet gives an area in ft², not ft.
  • Mixed units: enter every measurement in the same unit system — mixing feet and inches, or centimeters and meters, produces an incorrect area.

Real-world applications

  • Estimating material for a trapezoidal garden bed, deck section, or countertop
  • Cross-sections of drainage channels, embankments, and retaining walls in civil engineering
  • Roof sections, dormers, and other trapezoidal building elements in construction
  • Surveying irregular land parcels by splitting them into trapezoids and summing the areas

Frequently Asked Questions

What is the formula for the area of a trapezoid?
Area = ½ × (a + b) × h, where a and b are the lengths of the two parallel sides (the bases) and h is the perpendicular height between them. This is the same as multiplying the average of the two bases by the height.
What's the difference between a trapezoid's bases and legs?
The bases are the two parallel sides, labeled a and b in the area formula. The legs are the two non-parallel sides that connect the bases. Leg lengths are not needed to find the area, but they are needed to find the perimeter.
Why must each leg be at least as long as the height?
A leg is the hypotenuse of a right triangle formed by the height and the horizontal offset between the two bases. Since a hypotenuse is always the longest side of a right triangle, a leg can never be shorter than the height; a leg equal to the height means that side is perpendicular to the bases (a right trapezoid).
What is the midsegment of a trapezoid?
The midsegment (or median) is the line segment connecting the midpoints of the two legs. Its length always equals the average of the two base lengths, (a + b) / 2, regardless of the trapezoid's height or leg lengths.

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