📏 Enter known values

📐 Accepted units: mm, cm, dm, m, dam, hm, km, in, ft, yd, mi

Formula Reference

render

Worked example

Data
Base 1
\(b = {\color{#6c5ce7}{6\,\text{cm}}}\)
Base 2
\(c = {\color{#6c5ce7}{4\,\text{cm}}}\)
Height
\(d = {\color{#6c5ce7}{3\,\text{cm}}}\)
Area
\(a = \,?\)
Formula
\[a = \frac{\left({b}+{c}\right)\cdot{d}}{2}\]
Steps
1Substitute the values
\[a = \frac{\left({\color{#6c5ce7}{6\,\text{cm}}}+{\color{#6c5ce7}{4\,\text{cm}}}\right)\cdot{\color{#6c5ce7}{3\,\text{cm}}}}{2}\]
Each letter is replaced by its value.
2Add
\[a = \frac{10\,\text{cm}\cdot{\color{#6c5ce7}{3\,\text{cm}}}}{2}\]
\(6+4 = 10\)
3Multiply
\[a = \frac{30\,\text{cm}^{2}}{2}\]
\(10\cdot3 = 30\)\(\text{cm} \times \text{cm} = \text{cm}^{2}\)
4Divide
\[a = \frac{30\,\text{cm}^{2}}{2} = 15\,\text{cm}^{2}\]
\(\frac{30}{2} = 15\)
Area: 15 cm²
Check

If we use the result to calculate Base 1, we should get the value you entered:

\[b = \frac{2\cdot{a}}{{d}}-{c}\]
\[b = \frac{2\cdot15\,\text{cm}^{2}}{3\,\text{cm}}-4\,\text{cm} = 6\,\text{cm}\]
It gives 6 cm, the same as the value entered.
Calculate the Area
Please fill in the fields:
Base_1 Base_2 Height
And leave empty
Area
Calculate the Base_1
Please fill in the fields:
Area Base_2 Height
And leave empty
Base_1
Calculate the Base_2
Please fill in the fields:
Area Base_1 Height
And leave empty
Base_2
Calculate the Height
Please fill in the fields:
Area Base_1 Base_2
And leave empty
Height

How to calculate the area of a trapezoid

A trapezoid (called a trapezium in British English) has one pair of parallel sides, the bases. Its area is the average of the two bases times the height:

\[ \text{Area} = \frac{(\text{Base}_1 + \text{Base}_2) \times \text{Height}}{2} \]

The height is the perpendicular distance between the two bases, not the length of the slanted sides. Two copies of the same trapezoid, one of them turned upside down, form a parallelogram with base \( B_1 + B_2 \), and the trapezoid is half of it.

Formulas for the other values:

\[ \text{Height} = \frac{2 \times \text{Area}}{\text{Base}_1 + \text{Base}_2} \]

\[ \text{Base}_1 = \frac{2 \times \text{Area}}{\text{Height}} - \text{Base}_2 \]

How to use the calculator

  1. Enter three of the four values: the area, the two bases and the height.
  2. Leave empty the one you want to find.
  3. Press Calculate. It does not matter which base you enter as Base 1 and which as Base 2.

Worked examples

1. Bases of 8 cm and 5 cm and a height of 4 cm

\[ \text{Area} = \frac{(8 + 5) \times 4}{2} = 26\ \text{cm}^2 \]

2. Height of a trapezoid with an area of 45 m² and bases of 12 m and 6 m

\[ \text{Height} = \frac{2 \times 45}{12 + 6} = 5\ \text{m} \]

3. Missing base

A trapezoid has an area of 30 cm², a height of 5 cm and one base of 7 cm. The other base is \( \frac{2 \times 30}{5} - 7 = 12 - 7 = 5 \) cm.

4. A plot of land

A plot has two parallel boundaries of 40 m and 25 m that are 18 m apart. Its area is \( (40 + 25) \times 18 \div 2 = 585\ \text{m}^2 \).

Special cases

  • If both bases are equal, the trapezoid is a parallelogram and the formula becomes base × height.
  • If one base is 0, the trapezoid becomes a triangle and the formula becomes base × height ÷ 2.
  • The midsegment (the line joining the midpoints of the slanted sides) measures \( (B_1 + B_2) \div 2 \), so the area is also midsegment × height.
  • In an isosceles trapezoid with slanted sides \( s \), the height is \( \sqrt{s^2 - \left(\frac{B_1 - B_2}{2}\right)^2} \). With bases of 10 and 4 and sides of 5, the height is \( \sqrt{25 - 9} = 4 \) and the area is \( (10 + 4) \times 4 \div 2 = 28 \).

When Do You Need to Calculate the Area of a Trapezoid?

🏡 Land and Plot Measurement

Many plots, fields and lots have two parallel boundaries and two slanted ones. The trapezoid formula gives their area from three measurements without splitting the land into pieces.

Quick area for deeds, fencing quotes and taxes
🏠 Roofs and Gable Walls

Hip roofs have trapezoidal faces, and walls under a sloped roof are often trapezoids. Their area tells you how many shingles, panels or liters of paint to buy.

Avoids under-ordering roofing and cladding
🌊 Channels and Embankments

Irrigation channels, ditches and road embankments have a trapezoidal cross-section. Its area times the length gives the volume of earth to dig or the water the channel carries.

Key for earthworks and flow calculations
📊 Integrals and Data Analysis

The trapezoidal rule estimates the area under a curve by adding thin trapezoids. It is used to integrate measured data, such as speed over time to get distance.

Turns a table of readings into a total
👗 Sewing and Design

A-line skirts, lampshade panels and many bag patterns are cut from trapezoids. Their area tells how much fabric or material each piece uses.

Helps calculate the fabric for each pattern piece
📚 School Geometry

The area of a trapezoid is a classic geometry exercise, often combined with the Pythagorean theorem to find the height of an isosceles trapezoid.

Practice with averages, heights and right triangles

Common Mistakes

⚠️ Forgetting to Divide by 2
Common Error: Multiplying the sum of the bases by the height and stopping there. That is the parallelogram made of two trapezoids, twice the real area.
✅ Solution: Area = (B₁ + B₂) × h ÷ 2
⚠️ Using a Slanted Side as the Height
Common Error: The slanted sides are longer than the height unless they are vertical. Using one of them overestimates the area.
✅ Solution: The height is perpendicular to both bases
⚠️ Multiplying the Bases
Common Error: Writing B₁ × B₂ × h ÷ 2. The bases are added, not multiplied.
✅ Solution: Add the bases first, then multiply by the height
⚠️ Taking a Leg as a Base
Common Error: Entering one of the slanted sides as a base. The bases are the two parallel sides.
✅ Solution: Find the two parallel sides before entering the values
⚠️ Wrong Order When Solving for a Base
Common Error: Subtracting before dividing: 2 × A ÷ (h − B₂) instead of 2 × A ÷ h − B₂.
✅ Solution: First 2 × area ÷ height, then subtract the known base
⚠️ Different Units
Common Error: Bases in meters and the height in centimeters, common in plans with mixed measurements.
✅ Solution: Convert all lengths to the same unit

Applications by Industry

Construction
  • Roofing: Area of the trapezoidal faces of hip roofs
  • Retaining walls: Cross-section of walls that are wider at the base
  • Stairs: Side panels of landings and ramps
Civil & Hydraulic Engineering
  • Channels: Wet cross-section of trapezoidal canals to calculate the flow
  • Earthworks: Cut and fill volumes from trapezoidal profiles
  • Dams: Cross-section of embankment dams
Surveying & Agriculture
  • Plots: Area of fields with two parallel sides
  • Crop planning: Seed and fertilizer for a trapezoidal field
  • Irrigation: Surface covered by each sprinkler line
Mathematics & Data
  • Trapezoidal rule: Numerical integration of measured data
  • Physics: Distance from a speed–time graph with steady changes
  • Statistics: Area under ROC curves and cumulative charts
Automotive & Industry
  • Windows: Glass area of trapezoidal side windows
  • Sheet metal: Blanks cut as trapezoids for ducts and hoppers
  • Belts: Cross-section of V-belts
Design & Fashion
  • Patterns: A-line skirts and flared panels
  • Lampshades: Material for each panel of a tapered shade
  • Graphics: Rectangles drawn in perspective, which become trapezoids

External Resources

Other calculators

Surface Area of a Sphere
Surface Area of a Sphere
Circle Calculator
Circle Calculator
Surface Area of a Cylinder
Surface Area of a Cylinder
Area of a Circle
Area of a Circle
Area of a Rectangle
Area of a Rectangle
Area of a Triangle
Area of a Triangle
Area of a Rhombus
Area of a Rhombus
Area of a Cube
Area of a Cube

Geometry Calculators

Share this page with more people