[Maths Class Notes] on Centroid of a Trapezoid Formula Pdf for Exam

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.

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

 

Some Solved Questions by   

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{20times5}{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{16times4.5}{3times 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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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′.