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## Centroid of a Trapezoid Formulas – Find the Centroid of a Trapezium

Consider the following trapezium in which *AB || CD*. The trapezium *OABC* is placed such that the origin coincides with one of its vertices. *G* is its centroid. The lengths of its parallel sides are *AB = a* and *OC = b* and its height is *h*.

The coordinates of the centroid of the trapezium are given by the following formula.

Let’s look at an example to see how to use this formula.

**Question:** Find the centroid of a trapezium of height *5 cm* whose parallel sides are *6 cm* and *8 cm*.

**Solution:**a=6cm,b=8cm,h=5cm

Hence, the centroid is *2.38 cm* from the side whose length is *8 cm*.

Why don’t you try to solving a problem for practice?

**Question:** Find the centroid of a trapezium of height *4.5 cm* whose parallel sides are *4 cm* and *8 cm*.

**Options:**

(a) 2 cm from the side whose length is 4 cm

(b) 2 cm from the side whose length is 8 cm

(c) 3 cm from the side whose length is 4 cm

(d) 3 cm from the side whose length is 8 cm

**Answer:** (b)

**Solution:**a=4cm,b=8cm,h=4.5cm

Hence, the centroid is 2* cm* from the side whose length is *8 cm*.

## Centroid of a Trapezoid Formula

A trapezoid is a quadrilateral with two sides parallel. The centroid of a trapezoid lies between the two bases. For any trapezoid with parallel sides a and b, use below given formula.

Find below formula for the centroid of trapezoid located a distance of x,

Where,

h = Height of trapezoid

a, b = Length of parallel sides

## Solved Examples

**Example:**

If the parallel sides of trapezoid measures 8 cm, 10 cm and the height 9 cm, then find its centroid.

**Solution:**

Let a and b be the parallel sides of a trapezoid.

According to the given,

a = 8 cm, b = 10 cm and h = 9 cm

Using the centroid of trapezoid formula,

## FAQs (Frequently Asked Questions)

**Q1. What is a trapezoid?**

Ans: A trapezium or a trapezoid is a quadrilateral with at least one pair of parallel sides. The sides that are parallel to each other are called bases. The other sides are called legs. The legs may or may not be parallel to each other. Trapezoids are called Trapezium in the UK.

**Q2. How to calculate the area and perimeter of a trapezoid?**

Ans: The area and perimeter of a trapezoid can be calculated by using the formulas given below:

- Area: ½ x (sum of the lengths of the parallel sides) x perpendicular distance between parallel sides
- Perimeter: the sum of lengths of sides of a trapezoid

**Q3. Which website explains the centroid of a trapezoid formula clearly with examples?**

Ans: The centroid of a trapezoid formula can be found on Vedantu’s website. Vedantu has provided a simple explanation to calculate the centroid of a trapezium. All a student needs to do is follow the instructions line by line and practice example problems. Students can be assured that the formula is accurate as it is provided by top experts at Vedantu.

**Q4. What is the formula to find the centroid of a trapezium?**

Ans: The centroid of a trapezium lies between the two bases. The centroid of a trapezoid can be found out by using the formula given below:

x= {b+2a/3(a+b)}*h

Here,

h= height of the trapezoid

a, b= length of the parallel sides

Important Questions for CBSE Class 10 Maths Chapter 9 – Some Applications of Trigonometry

✅ Math Formulas ⭐️⭐️⭐️⭐️⭐

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