Centroid of Trapezoid

The centroid of a trapezoid is its center of mass, where the whole body mass is concentrated. In simpler words, if we consider a cutout of a trapezoid, the centroid is the point where it can be perfectly balanced on the tip of a pin.

Since it is a point, we normally find it as coordinates axes.

Formula

Let us solve an example to understand the concept better.

Find the centroid of a trapezoid given in the figure.

Solution:

As we know,
Centroid (G) = ${\left( \dfrac{h}{2},\dfrac{\left( a+2b\right) }{3\left( a+b\right) }\times h\right)}$ , here a = 12 cm, b = 7 cm, h = 7 cm
= (7/2, (12 + 2 × 7) × 7/3(12 + 7))
= (7/2, 26 × 7 / 57)
= (3.5, 3.193)
≈ (3.5, 3.2)