Trapezoid Formulas (Area, Median)

A trapezoid (UK: trapezium) is a quadrilateral with one pair of parallel sides, a and b. Its area is A = ½(a + b)h — the average of the two parallel sides times the perpendicular height h. The median equals (a + b)/2.

Trapezoid formulas

Area: $A = \tfrac{1}{2}(a + b)h$
Median: $m = \dfrac{a + b}{2}$

where a, b = the two parallel sides, h = height between the parallel sides, m = median (midsegment), A = area

Area

A = \tfrac{1}{2}(a + b)h

Worked example

A trapezoid with parallel sides 4 and 8 and height 5 has area 30 square units.

A = \tfrac12(a + b)h = \tfrac12(4 + 8)\cdot 5 = \tfrac12\cdot 60 = 30

Median

m = \dfrac{a + b}{2}

Interactive trapezoid explorer

Drag a slider (or type a value, or use the arrow keys) and watch the diagram, the results, and the full step-by-step substitution update live.

Parallel side a a

Parallel side b b

Height h

Area A 30units²

Median m 6units

Step-by-step substitution

A = ½(a + b)h = ½(4 + 8) · 5 = 30
median m = (a + b)/2 = (4 + 8)/2 = 6

Classroom use: trapezoid formulas

Who it's for: Grades 6–10 · Middle-school students learning the trapezoid area rule, and high-school students decomposing composite figures.

Learning objectives

After using this page, students will be able to:

Apply A = ½(b₁ + b₂)h to find trapezoid area.
Explain the formula as the average of the two parallel sides times the height.
Decompose a trapezoid into a rectangle and triangles to confirm the result.

Suggested classroom activity

Set b₁ = b₂ in the explorer and let students notice the formula collapse to the rectangle rule. Then set one base to zero and watch the triangle rule appear. Both special cases in one place make the "average of the bases" reading stick.

Standards alignment

Aligned to the Common Core State Standards for Mathematics. Codes are given exactly as published so they can be matched against state crosswalks.
Code	Standard
`6.G.A.1`	Find the area of triangles, special quadrilaterals, and polygons by composing or decomposing shapes.
`7.G.B.6`	Solve real-world problems involving area, volume, and surface area of 2-D and 3-D objects.

Free to use and adapt in class under the terms on our license page — no account, no sign-up, no ads. Content last reviewed August 2026.

Related & next steps

Add trapezoid to your formula sheet →

Frequently asked questions

What is the area formula for a trapezoid?

A trapezoid’s area is A = ½(a + b)h, the average of the two parallel sides (a and b) times the height h. For parallel sides 6 and 10 with height 4, the area is ½(16)(4) = 32.

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