Centroid of trapezium is bit tricky to determine. Because of different lengths **a & b** with having height **“h”.**

## Centroid of Trapezium Formula:

\(\bar{Y}= \frac{h}{3}\frac{(b+2a)}{(b+a)}\)Example

A trapezium shape is given whose dimensions are;

a = 6’, b = 8’, h = 5’

Find the centroid of trapezium.

### Solution

By using formula, centroid of trapezium can be easily determined:

\(\bar{Y}=\frac{5}{3}\frac{(8+2×6)}{(8+6)}\)\(\bar{y}= 2.38’=Answer\)

From where did the y¯ is measured? (from shorter side or longer side?

@ Adi: Take base of trapezoid as reference x-axis

What is the [bar{X}] ?