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.
Centroid of a Trapezoid Formula
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,
] Where,
h is the height
p is the base
q is the opposite parallel side
Comparing the values, we get:
XC = h/2
YC =
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,
] Where,
h = height
p and q are the two parallel sides
h = 4m
p = 5m
q = 3m
C = [4/2,
] C = [2, 44/24]
C = [2, 1.83]
Thus, the centroid is [2, 1.83] or 2m with respect to the x-axis and 1.83 m 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,
] Where,
h = height
p and q are the two parallel sides
h = 2cm
p = 6cm
q = 4cm
C = [2/2,
] C = [1, 28/30]
C = [1, 0.93]
Thus, the centroid is [1, 0.93] or 1cm with respect to the x-axis and 0.93cm 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,
] Where,
h = height
p and q are the two parallel sides
h = 10m
p = 7m
q = 4m
C = [10/2,
] C = [5, 150/33]
C = [5, 4.54]
Thus, the centroid is [5, 4.54] or 5m with respect to the x-axis and 4.54 m 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,
] Where,
h = height
p and q are the two parallel sides
h = 1cm
p = 2cm
q = 3cm
C = [1/2,
] C = [0.5, 8/15]
C = [0.5, 0.53]
Thus, the centroid is [0.5, 0.53] or 0.5cm with respect to x-axis and 0.53 cm 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,
] Where,
h = height
p and q are the two parallel sides
h = 8m
p = 5m
q = 3m
C = [8/2,
] C = [4, 88/24]
C = [4, 3.66]
Thus, the centroid is [4, 3.66] or 4m with respect to the x-axis and 3.66 m 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,
] Where,
h = height
p and q are the two parallel sides
h = 5m
p = 7m
q = 9m
C = [5/2,
] C = [2.5, 125/48]
C = [2.5, 2.60]
Thus, the centroid is [2.5, 2.60] or 2.5m with respect to the x-axis and 2.60m 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,
] Where,
h = height
p and q are the two parallel sides
h = 20cm
p = 15cm
q = 12cm
C = [20/2,
] C = [10, 780/81]
C = [10, 9.62]
Thus, the centroid is [10, 9.62] or 10cm with respect to the x-axis and 9.62 cm with respect to the y-axis.