Centroid of a Trapezoid Formula

The centroid of a trapezoid formula helps in calculating the position of the centroid of a trapezoid. A trapezoid is a quadrilateral with two parallel sides.The centroid of a trapezoid lies between the two bases. Let us understand the centroid of a trapezoid formula using solved examples.

What is Centroid of a Trapezoid Formula?

The centroid of a trapezoid formula to calculate the coordinates of centroid of a trapezoid is given as,

\(G = \left( \dfrac{h}{2}, \dfrac{(b+2a)}{3(a+b)}h\right) \)

where,

a, b = Length of the parallel sides

h = Distance between the parallel sides 

Examples Using Centroid of a Trapezoid Formula

Example 1: Find the centroid of a trapezoid of height 6 units, whose parallel sides are 4 units and 8 units.

Solution:

To find: Centroid of the given trapezium

Using the centroid of a trapezoid formula,

\(G = \left( \dfrac{h}{2}, \dfrac{(b+2a)}{3(a+b)}h\right) \)

Here,
h = 6 units
a = 4 units
b = 8 units

\(G = \left( \dfrac{6}{2}, \dfrac{(8+2\times 4)}{3(4+8)}6\right) = (3, 2.67)\)

Answer: The coordinates of centroid are given as (3, 2.67), or the centroid is 2.67 units from the side whose length is 8 units.

Example 2: Find the centroid of a trapezoid of height 10 units, whose parallel sides are 5 units and 3 units.

Solution:

To find: Centroid of the given trapezium

Using the centroid of a trapezoid formula,

\(G = \left( \dfrac{h}{2}, \dfrac{(b+2a)}{3(a+b)}h\right) \)

Here,
h = 10 units
a = 3 units
b = 5 units

\(G = \left( \dfrac{10}{2}, \dfrac{(5+2\times 3)}{3(3+5)}10\right) = (5, 4.58)\)

Answer: The coordinates of centroid are given as (5, 4.58), or the centroid is 4.58 units from the side whose length is 5 units.