Trapezoid Height Calculator

Created by Komal Rafay
Reviewed by Davide Borchia
Last updated: Sep 23, 2022

Omni's trapezoid height calculator is a convenient tool that allows you to determine the height of a trapezoid, but you already know that because the name says so.
Here you will not only learn how to find the height of a trapezoid using the trapezoid height formula but also how to calculate it without knowing the area.

Trapezoid height formula

The height of a trapezoid is the distance between its bases. And the bases are the parallel sides of the trapezoid.
There are two distinct methods of calculating the height of a trapezoid, when the area is known and when the area is unknown.
Let's dive into the details of these methods and look at their formulas:

The height of a trapezoid using the area

When calculating the height of a trapezoid using the area, you also need the measurement of the bases aa and bb in centimeters.
Another important thing to know is that the trapezoid height formula derives from the formula of the trapezoid area, which is:

A=(a+b)2h A = \frac {(a+b)}{2\cdot h}

Let's shuffle this formula to obtain our desired height of a trapezoid formula.

h=(a+b)2Ah = \frac {(a+b)}{2\cdot A}

where:

  • hh - Height of the trapezoid;
  • AA - Area of the trapezoid;
  • aa - 1ˢᵗ base of the trapezoid; and
  • bb - 2ⁿᵈ base of the trapezoid.

The height of a trapezoid without the area

We know that height of the trapezoid plays a role in identifying the area. In turn, the area would help determine the height of the trapezoid.

But what if we don't have the area and need to determine the height? You might find yourself in a tight spot, but we have got you covered.

There are two ways to estimate the height of a trapezoid without the area. They use the legs and angles of a trapezoid. The legs of a trapezoid are the non-parallel sides and are named cc and dd.

  • Using leg c and ∠α
    The first formula uses the leg c\text{leg}\ c and α∠α to determine the height of a trapezoid. The formula is:
    h=c×sinαh = c × \sin{ \angleα}

    where:

    • hh - Height of the trapezoid;
    • cc - Non-parallel leg c; and
    • sinsin - The sine function.
  • Using a leg and ∠δ
    The second formula uses the leg d\text{leg}\ d and δ∠δ to determine the height of a trapezoid. The formula is:
    h=d×sinδh = d × \sin{\angleδ}

    where:

    • dd - Non-parallel leg d.

Trapezoid height calculator

Our trapezoid height calculator is an easy-to-use tool that lets you calculate the height of a trapezoid in three different ways. Whether you know the area or not, we have got you covered.

The first method uses a leg and an angle. Here you have the option to input the legc\text{leg} c and α∠α. As a result, you have the height of a trapezoid in centimeters.
For instance, if you input 10 cm10\ \text{cm} in cc and 75°75° as the α∠α your height would be 9.6 cm9.6\ \text{cm}.

The second method is very similar to the first one. It also uses a leg and another angle. Here the legd\text{leg} d is used in combination with δ\angleδ and as a result, we get the height of the trapezoid.
So let's suppose you input 22cm22cm in legd\text{leg} d and δ\angle\delta is 95°95° then the height would be 21.916 cm21.916\ \text{cm}.

These two methods are independent of the area. Now, if you had the area of a trapezoid, you could use the third method. It uses the two bases a and b along with the area and gives you the height of the trapezoid.
For instance, the base aa is 21 cm21\ \text{cm}, base bb is 19 cm19\ \text{cm} and your area AA is 64 cm264\ \text{cm}^2 that gives the height as 3.2 cm3.2\ \text{cm}.

That should clear any doubt about how to find the height of a trapezoid or how to use the tool. Just give it a try.

FAQ

How can I find the height of a trapezoid?

There are three methods of calculating the height of a trapezoid.
The first two methods use the non-parallel sides and angles of a trapezoid to determine its height. They are:

  1. h = c × sin ∠α
  2. h = d × sin ∠δ

where:

  • h - Height of the trapezoid;
  • c - Non-parallel leg c;
  • d - Non-parallel leg d; and
  • sin - The sine function.

The third method uses bases a and b along with the area of a trapezoid to determine its height.
3. h = (a+b) / 2A
where:

  • a - Parallel base a;
  • b - Parallel base b; and
  • A - Area of the trapezoid.

Is trapezoid a rectangle?

Nope, but every rectangle is a trapezoid. It is the same as every square is a rectangle, but every rectangle is not a square.

A trapezoid is a quadrangle shape with at least a pair of parallel sides. The other pair of sides may or may not be parallel.
If 2 pairs of a quadrilateral shape are parallel then it is a rectangle.
The parallel sides of a trapezoid are known as bases and are referred to as a and b. The non-parallel sides are known as legs and referred to as c and d.

What is the height of a trapezoid if c = 15 cm and α = 65?

The height h = 13.595 cm if the leg c = 15 cm and α = 65°.
You can estimate the height of a trapezoid by using the formula:

h = c × sin ∠α

where:

  • h - Height of the trapezoid;
  • c - Non-parallel leg c; and
  • sin - The sine function.
Komal Rafay
A trapezoid with sides, angles and height marked
Using a leg and α
c (leg)
in
α
deg
Height (h)
in
Using a leg and δ
d (leg)
in
Angle4
deg
Height (h)
in
Using Area and bases
a (base)
in
b (base)
in
Area (A)
in²
Height (h)
in
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