Trapezoid Height Calculator

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.

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 $a$ and $b$ in centimeters.
Another important thing to know is that the trapezoid height formula derives from the formula of the trapezoid area, which is:

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

where:

• $h$ - Height of the trapezoid;
• $A$ - Area of the trapezoid;
• $a$ - 1ˢᵗ base of the trapezoid; and
• $b$ - 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 $c$ and $d$.

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

  where:

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

• Using a leg and ∠δ
  The second formula uses the $\text{leg}\ d$ and $∠δ$ to determine the height of a trapezoid. The formula is:
  $h = d × \sin{\angleδ}$

  where:

  • $d$ - Non-parallel leg d.

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 $\text{leg} c$ and $∠α$. As a result, you have the height of a trapezoid in centimeters.
For instance, if you input $10\ \text{cm}$ in $c$ and $75°$ as the $∠α$ your height would be $9.6\ \text{cm}$.

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

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 $a$ is $21\ \text{cm}$, base $b$ is $19\ \text{cm}$ and your area $A$ is $64\ \text{cm}^2$ that gives the height as $3.2\ \text{cm}$.

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.

Trapezoids are interesting shapes, so we have created so many interesting calculators around them.

Check them out!

• Trapezoid calculator
• Area of a trapezoid calculator
• Trapezoid perimeter calculator
• Trapezoid side calculator
• Trapezoid angle calculator
• Midsegment of a trapezoid
• Isosceles trapezoid calculator
• Isosceles trapezoid area calculator
• Right trapezoid calculator
• Right trapezoid area calculator
• Area of an irregular trapezoid calculator