Mathematics, Statistics & Geometry

Area of Trapezoid Calculator

Calculate the area of a trapezoid using its bases and height. Find the exact surface area and median length with full step-by-step workings.

Area
100
Median (Midsegment)12.5
Calculation StepsBase A (a) = 10 Base B (b) = 15 Height (h) = 8 Area = ((a + b) / 2) * h Area = ((10 + 15) / 2) * 8 Area = 100.000000

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Mastering the Trapezoid

The Area of Trapezoid calculator (also known as a Trapezium calculator) is an essential tool for measuring irregular four-sided shapes. Because many real-world objects have parallel top and bottom edges but slanted sides, the trapezoid formula is one of the most frequently used in construction and land measurement.

A=a+b2⋅h\begin{aligned} A = \frac{a + b}{2} \cdot h \end{aligned}

Where:
A=
The surface area of the trapezoid
a=
The length of one of the parallel sides (usually top)
b=
The length of the other parallel side (usually bottom)
h=
The perpendicular distance between the bases

How to Calculate Trapezoid Area

  1. Identify the Bases (a and b): These are the two sides that are parallel to each other.
  2. Measure the Height (h): The straight vertical distance between the bases (not the length of the slanted side).
  3. Apply the Formula: Area = [ (a + b) / 2 ] × h.

Types of Trapezoids

  • Isosceles Trapezoid: The non-parallel sides are equal in length.
  • Right Trapezoid: One of the non-parallel sides is perpendicular to the bases.
  • Scalene Trapezoid: All sides and angles are different.

Real-World Uses

  • Civil Engineering: Calculating the cross-sectional area of dams, canals, and drainage ditches.
  • Land Surveying: Estimating the area of plots that have one straight road boundary and one parallel back fence.
  • Architecture: Sizing slanted windows, gable ends, and roof sections.
  • Math and Physics: Using the "Trapezoidal Rule" to approximate the area under a curve in calculus.

Frequently Asked Questions

A trapezoid (or trapezium in British English) is a quadrilateral with at least one pair of parallel sides.

Add the lengths of the two parallel bases together, divide by 2 to get the average base length, and then multiply by the perpendicular height.

The median (or midsegment) is the line segment connecting the midpoints of the non-parallel sides. Its length is equal to (a + b) / 2.

Yes. The area formula A = ((a+b)/2) × h works for all types of trapezoids, including isosceles and right trapezoids.

A parallelogram has two pairs of parallel sides, whereas a trapezoid is only required to have one pair.

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