Isosceles Trapezoid Area Calculator

Created by Anna Szczepanek, PhD
Reviewed by Davide Borchia
Last updated: Jul 27, 2022

This isosceles trapezoid area calculator will help you deal with these very particular trapezoids. Recall that we say that a trapezoid is isosceles if its legs have the same length. You'll experience no trouble using Omni's isosceles trapezoid area calculator, but we know that life is hard and you sometimes have to calculate with pen and paper. Don't worry — we will teach you how to find the area of an isosceles trapezoid with the help of dedicated formulas.

What is the area of an isosceles trapezoid?

There are several dedicated isosceles trapezoid area formulas:

  • bases a,b and height h given: A = (a + b) * h / 2

  • bases a,b and leg c given: compute h via the Pythagorean Theorem (h is the square root of c² - (a-b)²/4) and A = (a + b) * h / 2

  • bases a,b and angle α given: compute h as tan(α) * (a-b)² / 4 and then A = (a + b) * h / 2

  • base a, leg c and angle α given: compute h as c * sin(α) and b as a - 2 * c * cos(α), then A = (a + b) * h / 2

Choose the isosceles trapezoid area formula that suits the data that is available (for notation, see the picture below). Or just use our isosceles trapezoid area calculator!

isosceles trapezoid

FAQ

How do I compute the area of an isosceles trapezoid given diagonal?

You can compute the area of an isosceles trapezoid as:

A = 0.5 × d² × sin(φ)

where:

  • A is the area of the trapezoid;
  • d is the length of a diagonal; and
  • φ is the angle between the diagonals.
Anna Szczepanek, PhD
A trapezoid with sides, angles and height marked
Longer base (a)
in
Shorter base (b)
in
Leg (c)
in
Height (h)
in
Diagonal (d)
in
Acute angle (α)
deg
Obtuse angle (β)
deg
Result
Area
in²
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