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Trapezoid Calculator

Area equals the quantity a plus b divided by 2 times h

Solution

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Calculate Trapezoid Area from Parallel Sides and Height

Use this form when both parallel sides and the perpendicular height between them are known. The formula averages the two parallel sides and multiplies by the height.

A = (a + b) / 2 × h

Calculate Trapezoid Top Side from Area, Bottom, and Height

Use this rearrangement when the area, bottom side, and height are known and you need the top parallel side.

a = 2A/h − b

Calculate Trapezoid Bottom Side from Area, Top, and Height

Use this rearrangement when the area, top side, and height are known and you need the bottom parallel side.

b = 2A/h − a

Calculate Trapezoid Height from Area and Parallel Sides

Use this rearrangement when the area and both parallel sides are known and you need the perpendicular height.

h = 2A / (a + b)

How It Works

This trapezoid calculator solves A = (a + b)/2 × h, where a and b are the two parallel sides and h is the perpendicular height between them. The midsegment m = (a + b)/2 — the segment connecting the midpoints of the two non-parallel sides — is always displayed as a supplementary output. Pick the unknown with the solve-for toggle and enter the remaining values in any supported length or area unit.

Example Problem

A trapezoid-shaped concrete slab has top side 4 m, bottom side 6 m, and perpendicular height 3 m. Compute its area.

  1. Knowns: a = 4 m, b = 6 m, h = 3 m
  2. Formula: A = (a + b) / 2 × h
  3. Compute the average of the parallel sides: (4 + 6) / 2 = 5 m (this is the midsegment m)
  4. Multiply by the height: A = 5 × 3 = 15 m²
  5. Sanity check (inverse): from A = 15, b = 6, h = 3, the top is a = 2A/h − b = 10 − 6 = 4 m ✓

The midsegment property means trapezoid area equals midsegment × height, exactly like a rectangle of those dimensions.

When to Use Each Variable

  • Solve for Area — when both parallel sides and the height are known — concrete pours, roofing, fabric patterns.
  • Solve for Top Side — when the area, bottom, and height are known and you need the missing top side.
  • Solve for Bottom Side — when the area, top, and height are known and you need the missing bottom side.
  • Solve for Height — when the area and both parallel sides are known and you need the perpendicular height.

Key Concepts

A trapezoid is a four-sided polygon with exactly one pair of parallel sides (the 'bases', conventionally a and b). The non-parallel sides are called 'legs'. The perpendicular height h is the distance between the two parallel bases, measured perpendicular to them. The midsegment m = (a + b)/2 is parallel to both bases and equal to their average. Special cases: when a = b, the trapezoid degenerates into a parallelogram (rectangle if angles are right); when a = 0, it degenerates into a triangle of base b and height h.

Applications

  • Construction: concrete slab pours, deck designs, and retaining-wall cross-sections
  • Civil engineering: irregular parcel area, road cross-sections, channel hydraulics
  • Geometry instruction: foundational area-formula derivation (the trapezoid formula reduces to many simpler cases)
  • Integration approximation: the trapezoidal rule approximates definite integrals as a sum of trapezoidal areas

Common Mistakes

  • Using the slant-leg length instead of the perpendicular height h — only the perpendicular distance between the bases contributes to area
  • Multiplying base × height directly without averaging the two parallel sides first — this gives the wrong answer unless a = b
  • Forgetting the /2 factor — A = (a + b) × h is off by a factor of 2
  • Confusing the midsegment with the height — midsegment is parallel to the bases, height is perpendicular

Frequently Asked Questions

How do you calculate the area of a trapezoid?

Use A = (a + b)/2 × h, where a and b are the parallel sides and h is the perpendicular height. For a trapezoid with a = 4 m, b = 6 m, h = 3 m, A = (4+6)/2 × 3 = 15 m².

What is the formula for the area of a trapezoid?

A = (a + b)/2 × h. Equivalently, A = m × h where m = (a + b)/2 is the midsegment. The area of a trapezoid is the midsegment times the perpendicular height — the same shape as a rectangle's area formula.

What is the midsegment of a trapezoid?

The midsegment is the line segment connecting the midpoints of the two non-parallel sides (the legs). Its length equals the average of the parallel sides: m = (a + b)/2. For a = 4 m and b = 6 m, m = 5 m.

How do you find the height of a trapezoid given the area and parallel sides?

Rearrange A = (a + b)/2 × h to h = 2A / (a + b). For A = 15 m², a = 4 m, b = 6 m: h = 30 / 10 = 3 m.

What's the difference between a trapezoid and a parallelogram?

A trapezoid has exactly ONE pair of parallel sides; a parallelogram has TWO. So a parallelogram is technically not a trapezoid in the exclusive definition (used in the US). The inclusive definition (used in many other countries) considers parallelograms a special case of trapezoid where both pairs of sides are parallel.

How do you find the missing parallel side of a trapezoid?

Rearrange to a = 2A/h − b or b = 2A/h − a. For A = 15 m², h = 3 m, b = 6 m: a = 2·15/3 − 6 = 10 − 6 = 4 m.

What is an isosceles trapezoid?

An isosceles trapezoid has the two non-parallel sides (legs) equal in length. This gives it a line of symmetry perpendicular to the parallel bases. The area formula is the same — A = (a + b)/2 × h — but the legs and base angles are constrained.

Can I use this calculator for a right trapezoid?

Yes. A right trapezoid has two right angles, so one leg is perpendicular to the bases — that leg equals the height h. The area formula A = (a + b)/2 × h applies unchanged; the additional structure just makes the height measurable directly along one leg.

Reference: Weisstein, Eric W. "Trapezoid." MathWorld — A Wolfram Web Resource. https://mathworld.wolfram.com/Trapezoid.html

Worked Examples

Concrete Pour

How much concrete fills a trapezoidal slab?

A trapezoid-shaped concrete pad has top side 4 m, bottom side 6 m, perpendicular height 3 m, and a 0.15 m depth. Find the surface area first, then the volume.

  • Knowns: a = 4 m, b = 6 m, h = 3 m
  • Formula: A = (a + b)/2 × h
  • A = (4 + 6)/2 × 3 = 5 × 3 = 15 m²
  • Volume at 0.15 m depth: V = 15 × 0.15 ≈ 2.25 m³

Surface area = 15 m²; concrete volume ≈ 2.25 m³

Add 5–10% waste for trim cuts and pump losses.

Roof Section

What is the area of a trapezoidal roof panel?

A roof panel has parallel edges 8 ft and 12 ft and a slope distance giving a 5 ft perpendicular height between the edges. Compute the area to estimate sheathing.

  • Knowns: a = 8 ft, b = 12 ft, h = 5 ft
  • Formula: A = (a + b)/2 × h
  • A = (8 + 12)/2 × 5 = 10 × 5 = 50 ft²

Area = 50 ft² (about 4.65 m²)

Sheathing material is usually ordered in 4 × 8 ft sheets — for 50 ft² that's about 1.6 sheets.

Inverse Solve

What height does a trapezoid need to enclose 24 m²?

An irrigation channel cross-section is a trapezoid with top width 6 m, bottom width 2 m, and a target cross-section area of 24 m². Find the required depth.

  • Knowns: A = 24 m², a = 6 m, b = 2 m
  • Formula: h = 2A / (a + b)
  • h = 2 · 24 / 8 = 6 m

Required depth = 6 m

Channels are often designed with the trapezoid inverted (narrow bottom, wider top) for stability; the formula is symmetric so top/bottom are interchangeable.

Trapezoid Formulas

A trapezoid is defined by two parallel sides a (top) and b (bottom) and the perpendicular height h between them. Area follows directly:

Area equals the quantity a plus b divided by 2 times hTop side a equals 2A over h minus bBottom side b equals 2A over h minus aHeight equals 2A over the quantity a plus b
Trapezoid with parallel sides a (top) and b (bottom) and perpendicular height hhab

Where:

  • A — area (m², ft², in²)
  • a — top parallel side (m, cm, in, ft, yd)
  • b — bottom parallel side
  • h — perpendicular height between the parallel sides
  • m — midsegment (m = (a + b)/2), parallel to the bases and equal to their average

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