Trapezoid Height Calculator
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Trapezoid height formulaTrapezoid height calculatorInteresting calculators about trapezoidsFAQsOmni'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 $a$ 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 nonparallel 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;
 $c$  Nonparallel 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:
 $d$  Nonparallel leg d.
Trapezoid height calculator
Our trapezoid height calculator is an easytouse 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.
Interesting calculators about trapezoids
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
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 nonparallel sides and angles of a trapezoid to determine its height. They are:
h = c × sin ∠α
h = d × sin ∠δ
where:
h
 Height of the trapezoid;c
 Nonparallel leg c;d
 Nonparallel leg d; andsin
 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; andA
 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 nonparallel 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
 Nonparallel leg c; andsin
 The sine function.