Area of a Trapezoid Calculator

Our area of a trapezoid calculator is the perfect tool to find the area of a trapezoid and determine its perimeter. All you need to do is enter the base and height of the trapezoid and the calculator will do the rest.

What is a Trapezoid?

A trapezoid is a quadrilateral with exactly one pair of parallel sides. In other words, it's a four-sided shape with two bases (the parallel sides) and two non-parallel sides called legs or lateral sides. The bases can be of different lengths, but the legs must have different lengths. If the bases and legs are all equal, it becomes a rectangle or a square, not a trapezoid.

Some key characteristics of a trapezoid:

• It has four straight sides.
• Exactly one pair of opposite sides are parallel.
• The other two sides are not parallel.
• The angles between the parallel and non-parallel sides can be different measures.

So a trapezoid has at least one pair of acute angles and at least one pair of obtuse angles, unless it's an isosceles trapezoid (where the non-parallel sides are equal), in which case it has two acute and two obtuse angles.

Area of a Trapezium Formula

The formula to find the area of a trapezoid is:

Area = (Sum of the parallel sides / 2) x Height

Or written mathematically:

A = (a + b) x h / 2

Where:

A is the area
a and b are the lengths of the parallel bases
h is the height (perpendicular distance between the bases)

This formula works for all types of trapezoids - isosceles, right-angled or scalene.

How Do I Find the Area of a Trapezoid?

To find the area of any trapezoid, follow these steps:

1. Identify and measure the parallel bases (a and b)
2. Measure the height (h) - the perpendicular distance between the bases
3. Substitute these values into the area formula: A = (a + b) x h / 2
4. Calculate and get your answer!

Let's go through an example:

Suppose the parallel bases of a trapezoid are 8 cm and 12 cm, and the height is 5 cm.

a = 8 cm
b = 12 cm
h = 5 cm

Putting these values in the formula:

A = (a + b) x h / 2
= (8 + 12) x 5 / 2
= 20 x 5 / 2
= 100 / 2
= 50 cm²

So the area of this trapezoid is 50 square centimeters.

You can see that for a trapezoid where a = b (and the trapezoid becomes a parallelogram), the area formula simplifies to A = b x h, which is the formula for the area of a rectangle.

How Do I Find the Perimeter of a Trapezoid?

The perimeter of any polygon is the total distance around it - simply the sum of all the side lengths. For a trapezoid with bases a and b, and legs c and d, the perimeter formula is:

Perimeter = a + b + c + d

To find it:

1. Measure all four side lengths (a, b, c, d)
2. Add them together using the formula above

For example, if a trapezoid has base lengths 7 cm and 11 cm, and leg lengths 5 cm and 8 cm:

a = 7 cm
b = 11 cm
c = 5 cm
d = 8 cm

Perimeter = a + b + c + d
= 7 + 11 + 5 + 8
= 31 cm

So the total perimeter of this trapezoid is 31 centimeters.

Trapezium vs Trapezoid

You may have noticed the term "trapezium" used instead of "trapezoid" in some places. This difference in naming conventions comes from British English versus American English:

• In British English, the term "trapezium" refers to what Americans call a "trapezoid" - a quadrilateral with one pair of parallel sides.
• In American English, "trapezoid" is used, while "trapezium" refers specifically to a quadrilateral with no parallel sides at all.

So generally, if you're using British English sources or speaking in the U.K., you'll see "trapezium" used in place of "trapezoid." The formulas and calculations are the same, just with different terminology.

FAQs

What if I don't know one of the base lengths?

If you don't know the length of one base but you know the other base length, the height, and one of the slanted side lengths, you can use trigonometry to calculate the missing base. However, that requires knowledge of more advanced math concepts.

Can a trapezoid have four equal sides?

No, if a quadrilateral has four equal sides, it is either a rhombus (if opposite sides are parallel) or a square (if all angles are also 90 degrees). A trapezoid must have two different lengths for the non-parallel sides.

How do I know if a quadrilateral is a trapezoid?

For a quadrilateral to be classified as a trapezoid, it must have exactly one pair of parallel sides. If it has zero or more than one pair of parallel sides, it is not a trapezoid.

Why is the formula for the area of a trapezoid important?

Understanding how to calculate the area of trapezoids is important for many real-world applications, such as:

• Finding areas of irregularly shaped fields or land plots
• Calculating material needs for construction projects
• Solving geometry problems
• Estimating areas in design, architecture, and engineering

So being able to find the area of trapezoids using the formula is a useful skill in many careers and everyday situations.

For more information, see Trapezoid on Wikipedia.