# Centroid of a Trapezoid

## What is Trapezoid?

In this article, students will be able to learn about the topic of the centroid of a trapezoid. We will also look at the centroid of the trapezoid formula. But before we learn how to find the centroid of a trapezoid, students need to focus on the basics and start from the beginning.

The first thing that one needs to learn is the definition of a trapezoid. A trapezoid can be defined as a quadrilateral in which there are two parallel sides. A trapezoid is also known as a trapezium. So, if you see trapezium written in some other book, then don’t be confused. It means the same thing as a trapezoid.

A trapezoid can also be defined as a four-sided figure that is closed. It also covers some areas and has its perimeter. We will learn the formula for both area and perimeter of a trapezoid at a later point in this article.

It should be noted that a trapezoid is a two-dimensional figure and not a three-dimensional figure. The sides that are parallel to one another are known as the bases of the trapezoid. On the other hand, the sides that are not parallel to each other are known as lateral sides or legs. The distance between the two parallel sides is also known as the altitude.

Some readers might find it interesting to learn that there is also a disagreement over the exact definition of a trapezoid. There are different schools of mathematics that take up different definitions.

According to one of those schools of mathematics, a trapezoid can only have one pair of parallel sides. Another school of mathematics dictates that a trapezoid can have more than one pair of parallel sides.

This means that if we consider the first school of thought to be true, then a parallelogram is not a trapezoid. But according to the second school of thought, a parallelogram is a trapezoid. There are also different types of trapezoids. And those different types of trapezoids are:

• Right Trapezoids

A right trapezoid contains a pair of right angles. We have also attached an image of a right trapezoid below.

• Isosceles Trapezoids

In an isosceles trapezoid, the non-parallel sides of the legs of the trapezoid are equal in length. An image depicting an isosceles trapezoid is attached below.

• Scalene Trapezoids

A scalene trapezoid is a figure in which neither the sides nor the angles of the trapezium are equal. For your better understanding, an image of a scalene trapezoid is attached below.

## The Formula for Area and Perimeter of a Trapezoid

Now, let’s look at the formula for calculating the area and perimeter of a trapezoid. According to experts, the area of a trapezoid can be calculated by taking the average of the two bases and multiplying the answer with the value for the altitude. This means that the formula for the area of a trapezoid can also be depicted by:

Area = ½(a + b) x h

Moving on to the formula for the perimeter of a trapezoid, it can be described as the simple sum of all the sides. This means that if a trapezoid has four sides like a, b, c, and d, then the formula for the perimeter of a trapezoid can be represented by:

Perimeter = a + b + c + d.

### The Properties of a Trapezoid

There are various important properties of a trapezoid. We have discussed those properties in the list that is mentioned below.

• The diagonals and base angles of an isosceles trapezoid are equal in length.

• If a median is drawn on a trapezoid, then the median will be parallel to the bases. And the length will also be the average of the length of the bases.

• The intersection point of the diagonals is collinear to the midpoints of the two opposite sides.

• If there is a trapezoid that has sides, including a, b, c, and d, and diagonals p and q, then the following equation stands true.

p2 + q2 = c2 + d2 + 2ab

In the next section, we will look at the centroid of a trapezoid formula.

### The Formula for Centroid of a Trapezoid

In this section, we will look at the trapezoid centroid and the centroid formula for the trapezoid. As you must already know, a trapezoid is a quadrilateral that has two sides parallel. The centroid, as the name indicates, lies at the centre of a trapezoid. This means that for any trapezoid that has parallel sides a and b, the trapezoid centroid formula is:

X = {b + 2a / 3 (a + b)} x h

In this formula, h is the height of the trapezoid. Also, a and b are the lengths of the parallel sides.

Question 1. Define What You Understand by a Trapezoid.

Answer: A trapezoid is a polygon with four sides. There are two parallel and two non-parallel sides in this figure. Trapezoids are also known as trapeziums in some cases.

Question 2. What is the Formula for Calculating the Area of a Trapezoid?

Answer: The area of a trapezoid can be calculated by taking the average of the two parallel bases and multiplying the answer with the value of the altitude or the distance that exists between the two parallel sides. The formula for calculating the area of a trapezoid is:

Area = ½(a + b) x h.

Question 3. Can You State that a Trapezoid is a Quadrilateral?

Answer: Yes, a trapezoid can be classified as a quadrilateral as it has four sides. Two sides are parallel, and the remaining two sides are not parallel.

Question 4. Mention any Three Attributes of a Trapezoid.

Answer: The three primary attributes of a trapezoid are:

• The diagonals and base angles of an isosceles trapezoid are equal in length.

• The opposite sides of an isosceles trapezoid are of the same length. It can also be said that the sides are congruent to one another.

• The intersection point of the diagonals are collinear to the midpoints of the two opposite sides.

Question 5. Calculate the Centroid of a Trapezoid, Which has the Following Dimensions.

A = 12’, b = 5’, and h = 5’.

Answer: We know that the values for a = 12’, b = 5’, and 5 = 5’

This means that if we use the centroid of the trapezoid formula, then we will get:

X = {b + 2a / 3 (a + b)} x h

X = {5 + 2 x 12 / 3 (12 + 5)} x 5

X = 2.84

Hence, the value of the centroid of the trapezoid is at a distance of 2.84’.

Question 6. There is a Trapezoid in Which the Parallel Sides Measure 8 cm and 10 cm. The Height of the Trapezoid is 9 cm. Use this Information to Find the Centroid.

Answer: Let’s assume that a and b are two parallel sides of a trapezoid. This means that a = 8 cm, b = 10 cm, and h = 9 cm.

By using the centroid of a trapezoid formula, we will get:

X = {b + 2a / 3 (a + b)} x h

X = {10 + 2 (8) / 3 (8 + 10)} x 9

X = {26 / 54} x 9

X = 13 / 3

X = 4.33