Isosceles Trapezoid Area Calculator

Q: 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.

Creators

Anna Szczepanek, PhD

Anna SzczepanekPhD, Jagiellonian University in Kraków, Poland

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Anna Szczepanek, PhD is a mathematician at the Faculty of Mathematics and Computer Science of the Jagiellonian University in Kraków, where she researches mathematical physics and applied mathematics. At Omni, Anna uses her knowledge and programming skills to create math and statistics calculators. In her free time, she enjoys hiking and reading. See full profile

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Reviewers

Davide Borchia

Physicist by education, scientist by vocation. He holds a master’s degree in complex systems physics with a specialization in quantum technologies. If he is not reading something, he is outdoors trying to enjoy every bit of nature around him. He uses his memory as an advantage, and everything you will read from him contains at least one “I read about this five years ago” moment! See full profile

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

Useful trapezoid resources

Besides the isosceles trapezoid area calculator, Omni has a vast collection of trapezoid-related tools. Make sure to take a look at:

FAQs

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.