# Trapezoid Calculator

Welcome to the trapezoid calculator, a tool with which you'll be able to:

- Calculate the trapezium
**area**; - Find the trapezoid
**height**; - Calculate the trapezoid
**perimeter**; and - Calculate the trapezoid
**angles**.

Read on if you want to learn how to find the trapezoid height, area, or perimeter using the formulas.

## Trapezoid perimeter and angles

### Perimeter

The perimeter of a polygon, be it regular or irregular, is the **sum of its side lengths**, and **trapezoids** are not the exception. Therefore, the **perimeter of a trapezoid is the sum of its four sides**:

**P = a + b + c + d**

### Angles

Like any other quadrangle, the sum of **angles** in a trapezoid is 360 degrees (or 2π radians). However, being a trapezoid (i.e., having a pair of parallel sides) forces an additional property, which says that the pair of angles along one of the legs are supplementary angles. Therefore, their sum must equal 180 degrees (or π radians), which in notation from the calculator figure, translates into:

**α + 𝛾 = β + δ = 180°**

## How to calculate trapezoid area

A trapezium is like a rectangle that has "fallen over" slightly. Therefore, we calculate its area in a similar way to the area of a rectangle.

To calculate a trapezoid area, use the following formula:

**A = h × (a + b)/2**

where:

— Trapezium area;**A**— Trapezoid height; and**h**and**a**— Trapezoid bases.**b**

You can look at the dimensions in the following image:

For example, to calculate the area of a trapezoid whose bases are **a =****6 in** and **b =****5 in** with height **h =****4 in**:

**A =****4 in × (6 in + 5 in)/2**

**A =****4 in × (11 in)/2**

**A =****4 in × 5.5 in**

**A =****22 in ^{2}**

If the formula seems confusing to you, you can follow these steps to obtain the result:

- Sum the bases of the trapezoid. In this case:
**a + b****= 6 in + 5 in = 11 in** - Divide the previous result by two. In this case:
**(11 in)/2 = 5.5 in** - Multiply the previous result by the height. In this case:
**4 in × 5.5 in = 22 in**

**But what if you don't know h?** Let's see how to find the trapezoid height.

## How to find the height of a trapezoid

The equation to find the height relies on trigonometric functions. The formula is:

**h = c × sin(α) = d × sin(δ)**

As you can see, to calculate the height, you need to know:

- The side
and the angle**c**; or**α** - The side
and the angle**d**.**δ**

An acute trapezoid | An obtuse trapezoid |

For example, to calculate the height of a triangle with * c = 5 in* and

*:*

**α = 22 degrees****h =****5 in × sin(22°)**

**h =****= 5 in × 0.3746**

**h =****= 1.873 in**

You can learn more about trigonometric functions with our trigonometric functions calculator.