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Centroid of a Trapezoid Formula

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Last updated date: 14th Apr 2024
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Centroid of a Trapezoid Formulas - Find the Centroid of a Trapezium

Consider the following trapezium in which AB || CD. The trapezium OABC is placed such that the origin coincides with one of its vertices. G is its centroid. The lengths of its parallel sides are AB = a and OC = b and its height is h.

The coordinates of the centroid of the trapezium are given by the following formula.

  • \[G\left ( \frac{h}{2},\frac{b+2a}{3(a+b)}h \right )\]

Let’s look at an example to see how to use this formula.

 

Some Solved Questions by Vedantu  

Question: Find the centroid of a trapezium of height 5 cm whose parallel sides are 6 cm and 8 cm.

Solution:

a=6cm,b=8cm,h=5cma=6cm,b=8cm,h=5cm

\[Gy=\frac{b+2a}{3(a+b)}h\]\[=\frac{8+12}{3(8+6)}\times5\]\[=\frac{20\times5}{42}\]=2.38cm

Hence, the centroid is 2.38 cm from the side whose length is 8 cm.

Why don’t you try to solve a problem for practice?

Question: Find the centroid of a trapezium of height 4.5 cm whose parallel sides are 4 cm and 8 cm.

Options:

(a) 2 cm from the side whose length is 4 cm

(b) 2 cm from the side whose length is 8 cm

(c) 3 cm from the side whose length is 4 cm

(d) 3 cm from the side whose length is 8 cm 

Answer: (b)

Solution:

a=4cm,b=8cm,h=4.5cma=4cm,b=8cm,h=4.5cm

\[Gy=\frac{b+2a}{3(a+b)}h\]\[=\frac{8+8}{3(8+4)}\times4.5\]\[=\frac{16\times4.5}{3\times 12}=\frac{72}{36}=2cm\]

Hence, the centroid is 2 cm from the side whose length is 8 cm.

 

What Exactly is a Centroid? Definition of a Centroid

A centroid, also known as a geometric center, is the center of mass of a uniformly dense object. To make it easier to understand, think of it as the point where you should place the tip of a pin in order to balance your geometric shape on it.


Formula for the Centroid of a Trapezoid

The centroid of a trapezoid formula can be used to determine the position of a trapezoid's centroid. A quadrilateral with two parallel sides is known as a trapezoid. A trapezoid's centroid is located halfway between the two bases. Let's look at a few examples of the centroid of a trapezoid formula.

A trapezoid is a four-sided quadrilateral with two parallel sides. A trapezoid's centroid is located halfway between the two bases. Use the formula below to find any trapezoid with parallel sides a and b.


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Find the formula for the centroid of a trapezoid at a distance of x in the table below.

\[x=\frac{b+2a}{3(a+b)}h\]

Where,

h = Trapezoid height

a, b = Parallel side lengths


Calculator for Centroid

Simply enter the vertices of your shape as Cartesian coordinates to utilize this centroid calculator. Let's look at how to find the trapezoid's centroid:

  • Select the sort of form for which you want the centroid to be calculated. In this scenario, we'll go with an N-sided polygon.

  • Fill in the N parameter (if required). For our example, we'll need to know how many sides a polygon has. We type 4 into the N box since the trapezoid is a quadrilateral.

  • After that, the fields for entering coordinates will display. Enter the vertices of your shape's coordinates. Assume that the vertices of our trapezoid are:

    • A = (1,1)

    • B = (2,4)

    • C = (5,4)

    • D = (11,1)


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  • The result will be displayed on our centroid calculator! The choice of a trapezoid's centroid is (4.974,2.231).

Example: Find the centroid of the trapezoid with the following dimensions: a = 12′, b = 5′, and h = 5′.

Solution: Given,

a = 12′; b = 5′; h = 5′

Using centroid of trapezoid formula,

x = \[\frac{b + 2a}{3(a + b)} × h\]

x = \[\frac{5 + 2 \times 12}{3(12 + 5)} × 5\]

x = 2.84

As a result, the trapezoid's centroid is at a distance of 2.84′.

FAQs on Centroid of a Trapezoid Formula

1. What is a trapezoid?

A trapezium or a trapezoid is a quadrilateral with at least one pair of parallel sides. The sides that are parallel to each other are called bases. The other sides are called legs. The legs may or may not be parallel to each other. Trapezoids are called Trapezium in the UK. You can download the free pdf of Centroid of a Trapezoid Formula | Find the Centroid of a Trapezium from Vedantu and learn the concepts and meaning of the Trapezium in a better way. Regular learning can make you understand the concepts properly.

2. How to calculate the area and perimeter of a trapezoid?

The area and perimeter of a trapezoid can be calculated by using the formulas given below:

Area: ½ x (sum of the lengths of the parallel sides) x perpendicular distance between parallel sides

Perimeter: the sum of lengths of sides of a trapezoid. Students are required to solve problem equations sums based on the area and perimeter of a trapezoid. You can learn with the help of pdf of Centroid of a Trapezoid Formula | Find the Centroid of a Trapezium. 

3. Which website explains the centroid of a trapezoid formula clearly with examples?

The centroid of a trapezoid formula can be found on Vedantu’s website. Vedantu has provided a simple explanation to calculate the centroid of a trapezium. All a student needs to do is follow the instructions line by line and practice example problems. Students can be assured that the formula is accurate as it is provided by top experts at Vedantu. The formulations of the topics are easy to read and understandable. You can download the PDF and start learning with Vedantu. 

4. What is the formula to find the centroid of a trapezium?

The centroid of a trapezium lies between the two bases. The centroid of a trapezoid can be found out by using the formula given below:\[x=\frac{b+2a}{3(a+b)}\times h\]. Here, h= height of the trapezoid, a, b= length of the parallel sides. These are also the important Questions for CBSE Class 10 Math Chapter 9 - Some Applications of Trigonometry. Students should be thorough with the formula to find the centroid of a trapezium. You can learn better with the help of experts at Vedantu.

5. Is the Centroid of a Trapezoid Formula | Find the Centroid of a Trapezium helpful?

Yes, the Centroid of a Trapezoid Formula | Finding the Centroid of a Trapezium is helpful. It can help students to know the concepts of the centroid of a trapezium, its formula and how to find the centroid of the trapezium. We have drafted a set of complex questions on the trapezium formula. Students are required to learn and practice these problem equations daily and it can help them to understand the concepts in a better way. Regular practice can make you an expert in the chapter on trapezium centroid.