# Area of ​​a trapezoid - different ways to calculate the area - help with calculation (2023)

Finding the area of ​​different shapes like trapezoids may seem difficult at first because of their shapes. However, all you need is the right formula to calculate the area of ​​a trapezoid. The realm covers a dimensional space that it occupies.

In this article, we define what a trapezoid is and show different ways to find areas.

## What is a trapeze?

A trapezoid is a quadrilateral with several parallel sides. The quadrilateral has four parts, but if it has a pair of parallel sides, it is a trapezoid. However, if both pairs of sides are parallel, it is a parallelogram.

Some of the properties of a trapezoid are:

• No angles, sides and diagonals.

are congruent

• Parallel bases mean AB/CD

• four parts

• Each bottom base angle complements each other
the angle of the upper base on a similar side

What is a trapeze?

What is an isosceles trapezoid?

What is the origin of the word trapeze?

How to calculate the area of ​​a trapezoid

What if you have the median?

(Video) Area of a Trapezoid (Trapezium) | Math with Mr. J

Find the area of ​​a trapezoid without the length of a parallel side

Calculation of missing values

How to calculate the height if you have the area

trapezoidal applications

final thoughts

## What is an isosceles trapezoid?

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An isosceles trapezoid is a single trapezoid with legs of equal length, where the legs are non-parallel sides. Some properties of the isosceles trapezoid are:

• congruent diagonal

• The properties of the trapezoid work through
Definition

• The bottom and top corners of the base are
congruent

## What is the origin of the word trapeze?

picture ofGeraldo

Euclid wrote his work on geometry around 300 BC. in his book; He used the word trapezoid to name a four-sided figure that was not a rhomboid, rectangle, or rhombus. Later, the name gained a Latin translation to now trapezoidal.

Later, Proclus, a geometer, incorporated specific refinements to Euclid's work that have now become fundamental concepts in geometry. Proclus found a new meaning for trapezoid, referring to any four-sided figure with two parallel sides.

(Video) Area of a Trapezoid | MathHelp.com

Later, the geometer invented a new term, trapezoid, denoting a four-sided figure with no two parallel sides. In 1795, however, an English mathematician, Charles Hutton, reversed the descriptions. The United States still follows Hutton's definition, although the British have reverted to Proclus' original meaning.

## How to calculate the area of ​​a trapezoid

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To calculate the area of ​​a trapezoid, you need a formula. Find the length of the non-parallel side, the height of the trapezoid, and the length of one base. The height of a trapezoid is the diagonal line that runs from one corner to the opposite side.

The basic formula is (B1+B2)x1/2x(H)

• where B1 is the upper parallel
trapeze length

• where B2 is the lower parallel
trapeze length

• where H is the height of the
trapeze

You can also find the area of ​​a trapezoid by dividing it into two triangles and a rectangle. At this point you need to calculate the area of ​​both triangles and find the area of ​​the rectangle. Add these two together to get the area of ​​the trapezoid.

The formula for calculating the area of ​​the triangle is ½ (b-a)h, where b is the length minus the height and h is the height of the triangle.

The formula for creating the area of ​​the rectangle is ah, where a is the length of the triangle and h is the height.

For example, if the height of the trapezoid is 8 cm, the height of the bottom is 14 cm, and its height is 4 cm, then you get a rectangle 8 cm long and 4 cm high.

The triangle is 6 cm long if you subtract 14 cm from 8 cm. The height of the triangle remains 4 cm.

Now to find the area of ​​the trapezoid you need the area of ​​the two triangles and the area of ​​the rectangle.

The area of ​​the triangle = (6X4)/2=12

The area of ​​the rectangle = (8X4)=32

Add these two areas to get 44 cm2 to get the area of ​​a trapezoid.

You can also use the above formula ½ (b1+b2) h ½ (14+8) x4=44cm2

## What if you have the median?

You can find the area of ​​a trapezoid if you have
Median The median is the line segment that joins the midpoints of
non-parallel sides. Also, the median is the average of two parallel sides.

If you have the median and magnitude, you can
Find the area of ​​a trapezoid using the formula:

A=mh where h is the height and m is the median.

(Video) ⏢ Calculate trapezoid area! Easily learn how to calculate the area of the trapezoid 😊

## Find the area of ​​a trapezoid without the length of a parallel side

picture ofjosue_seajw92josue_seajw92​​​

In some cases, you may only have the length of the diagonal, the length of the diagonal, the height of the trapezoid, and a non-parallel side. Now you need to calculate the area of ​​the trapezoid. Fortunately, you can calculate the area even if you only have one non-parallel side.

All you need is to find the length of the base, the height and the distance of the given non-parallel side. if you for example
If you have a trapezoid with a height of 4 inches, an unparallel side of 5 inches, and a base of 6 inches, you need to determine the length of the other side.

If the trapezoid is 8 inches diagonally, use the Pythagorean theorem to find the length of the unknown side.

The formula is (a x 2) + (b x 2) = (C x 2)

The letters a and b represent the other two sides, and c is the hypotenuse.

With the trapezoid, you have two triangles. The sum of the two unknown sides of triangles is the length of the hidden side. Use the Pythagorean formula to find the unknown sides.

The second triangle will be 6 inches long and the first triangle will be 3 inches long. Add inches to both to get the
Unknown base length as 9 inches.

Now find the area of ​​a trapezoid, ½ (b1 + b2) h = ½ (6 + 9) 4 = 30 inches.

Find the area of ​​a trapezoid with no parallel sides

Sometimes it may be necessary to find the area of ​​a trapezoid that has no parallel sides. First you need to divide the trapezoid into two triangles.

The next step is to get the values ​​for a side angle, one side you know and the other side specified. You can name the sides a, b and c. Every triangle has all sides up.

Use the formula to calculate the areas of triangles

A=be/2 (Sen x a)

Substitute the values ​​of a, b, and c into the formula to find the area of ​​both triangles. Add the areas of the triangles to get the area of ​​a trapezoid with no parallel sides.

## Calculation of missing values

picture ofKaboo-mpics

You may need to calculate the base or height if you have the area. This is how you get the missing values.

(Video) How To Find, Calculate The Area Of A Trapezoid - Formula For The Area Of A Trapezoid Explained

### How to calculate the height if you have the area

picture ofMiraCosicName

Although you can sometimes calculate the area using a standard formula, you may need to calculate the height when obtaining the area. To do this, you need to transpose using the traditional method.

You can use algebra to figure out the formula. For example, to get the height, you can use the formula:

H=2A/(a+b)

where A is the area and a, b are two bases.

To get the base value, you need the height, area, and two bases. Rearrange the main formula to get the base.

The formula is:

B=2A/ (h)-a where A is the area of ​​the trapezoid and a is one of the sides of the trapezoid.

## trapezoidal applications

picture ofnew day

In biology, you'll find terms like trapeze or trapeze that refer to specific organs or shapes. Also in architecture, the term can be found in symmetrical buildings, windows, doors with a wide base that tapers towards the top.

The windows in the A-frame gables resemble trapezoids, with the bottom sides being horizontal and the parallel sides running from left to right.

If you look at the Egyptian architectural style, you will see that most of its features are in the shape of an isosceles trapezoid with straight sides and square corners. Inca has this standard style for its windows and doors.

Truss bridges have multiple trapezoids that connect the base of the bridge to the upper structure. Aluminum or steel supports form adjacent trapezoids with parallel sides that form the bottom and top of the bridge.

In Geometry you will find that the cross ladder problem is the method of finding the distance between the parallel sides of the right trapezoid given the distance from the vertical; Basis for oblique intersection and the lengths of diagonals.

Most bags have two trapezoids as the long sides of the bag. You'll notice that the top and bottom are parallel, although the top edge is shorter than the bottom edge.

## final thoughts

Calculating the area of ​​a trapezoid is not complicated. All you need is to use the above formula. Alternatively, you can split the trapezoid into two triangles and a rectangle. Find the area of ​​the triangles and add it to the area of ​​the rectangle.

Additionally, you can use trigonometric functions like tangent, cosine, and sine to find the missing sides of any triangle. These functions work even if you know the angles of the trapezoid.

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(Video) Area of a Trapezoid

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