Centroid of a Trapezoid Formula

A trapezoid is a type of quadrilateral with two parallel sides. A quadrilateral is a type of polygon with four sides. The sum of four internal angles of a quadrilateral is 360°. Centroid refers to the center point of any figure. It is also known as the geometric center. In a 2D coordinate system, the centroid is always measured with respect to the x-axis and y-axis. In a trapezoid, the centroid is also measured with respect to these two axes.

Table of Contents

A centroid point is the center point of the trapezoid. Centroid is represented in the form of coordinates of the center point of a trapezoid. A horizontal or vertical line through the centroid point divides it into two equal parts. It means, for the height ‘h,’ a center point will be ‘h/2.’ Similarly, the other center point is calculated. These two points form the centroid.

The diagram of a trapezoid is shown below:

Centroid of a figure is given by:

C = [XC, YC]

Where,

XC is the point on the x-axis

YC is the point on the y-axis

The formula to calculate the centroid of a trapezoid is given by:

C = [h/2, $\frac{(q + 2p)h}{3(p + q)}$ ]

Where,

h is the height

p is the base

q is the opposite parallel side

Comparing the values, we get:

XC = h/2

YC = $\frac{(q + 2p)h}{3(p + q)}$

Sample Problems

Question 1: Find the centroid of a trapezoid with a height of 4m and two parallel sides of 5m and 3m.

Solution:

The formula to calculate the centroid of a trapezoid is given by:

C = [h/2, $\frac{(q + 2p)h}{3(p + q)}$ ]

Where,

h = height

p and q are the two parallel sides

h = 4m

p = 5m

q = 3m

C = [4/2, $\frac{(3+ 2\times5)4}{3(5 + 3)}$ ]

C = [2, 52/24]

C = [2, 2.17]

Thus, the centroid is [2, 2.17] or 2m with respect to the x-axis and 2.17m with respect to the y-axis.

Question 2: Find the centroid of a trapezoid with a height of 2cm and two parallel sides of 6cm and 4cm.

Solution:

The formula to calculate the centroid of a trapezoid is given by:

C = [h/2, $\frac{(q + 2p)h}{3(p + q)}$ ]

Where,

h = height

p and q are the two parallel sides

h = 2cm

p = 6cm

q = 4cm

C = [2/2, $\frac{(4 + 2 \times 6)2}{3(6 + 4)}$ ]

C = [1, 32/30]

C = [1, 1.07]

Thus, the centroid is [1, 1.07] or 1cm with respect to the x-axis and 1.07cm with respect to the y-axis.

Question 3: Find the centroid of a trapezoid with a height of 10m and two parallel sides of 7m and 4m.

Solution:

The formula to calculate the centroid of a trapezoid is given by:

C = [h/2, $\frac{(q + 2p)h}{3(p + q)}$ ]

Where,

h = height

p and q are the two parallel sides

h = 10m

p = 7m

q = 4m

C = [10/2, $\frac{(4 + 2 \times 7)10}{3(7 + 4)}$ ]

C = [5, 180/33]

C = [5, 5.45]

Thus, the centroid is [5, 5.45] or 5m with respect to the x-axis and 5.45m with respect to the y-axis.

Question 4: Find the centroid of a trapezoid with a height of 11cm and two parallel sides of 3cm and 2cm.

Solution:

The formula to calculate the centroid of a trapezoid is given by:

C = [h/2, $\frac{(q + 2p)h}{3(p + q)}$ ]

Where,

h = height

p and q are the two parallel sides

h = 1cm

p = 2cm

q = 3cm

C = [1/2, $\frac{(3 + 2 \times 2)1}{3(2 + 3)}$ ]

C = [0.5, 7/15]

C = [0.5, 0.47]

Thus, the centroid is [0.5, 0.47] or 0.5cm with respect to x-axis and 0.47cm with respect to y-axis.

Question 5: Find the centroid of a trapezoid with a height of 8m and two parallel sides of 5m and 3m.

Solution:

The formula to calculate the centroid of a trapezoid is given by:

C = [h/2, $\frac{(q + 2p)h}{3(p + q)}$ ]

Where,

h = height

p and q are the two parallel sides

h = 8m

p = 5m

q = 3m

C = [8/2, $\frac{(3 + 2 \times 5)8}{3(5 + 3)}$ ]

C = [4, 104/24]

C = [4, 4.33]

Thus, the centroid is [4, 4.33] or 4m with respect to the x-axis and 4.33m with respect to the y-axis.

Question 6: Find the centroid of a trapezoid with a height of 5m and two parallel sides of 7m and 9m.

Solution:

The formula to calculate the centroid of a trapezoid is given by:

C = [h/2, $\frac{(q + 2p)h}{3(p + q)}$ ]

Where,

h = height

p and q are the two parallel sides

h = 5m

p = 7m

q = 9m

C = [5/2, $\frac{(9 + 2 \times 7)5}{3(7 + 9)}$ ]

C = [2.5, 115/48]

C = [2.5, 2.4]

Thus, the centroid is [2.5, 2.4] or 2.5m with respect to the x-axis and 2.4m with respect to the y-axis.

Question 7: Find the centroid of a trapezoid with a height of 20cm and two parallel sides of 15cm and 12cm.

Solution:

The formula to calculate the centroid of a trapezoid is given by:

C = [h/2, $\frac{(q + 2p)h}{3(p + q)}$ ]

Where,

h = height

p and q are the two parallel sides

h = 20cm

p = 15cm

q = 12cm

C = [20/2, $\frac{(12 + 2 \times 15)20}{3(15 + 12)}$ ]

C = [10, 840/81]

C = [10, 10.37]

Thus, the centroid is [10, 10.37] or 10cm with respect to the x-axis and 10.37cm with respect to the y-axis.

Last Updated :
10 Feb, 2022

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Centroid of a Trapezoid Formula