Centroid of a Trapezoid Formula: Definition & Solved Examples

Trapezoid is a quadrilateral in which one pair of opposite sides are parallel while the other pair of sides is non-parallel. A trapezoid is also referred to as a trapezium. The parallel pair of sides is known as the base of the trapezium and the non-parallel pair of sides is called the legs of a trapezium. 

Centroid of Trapezoid is the center point of the trapezoid. It is represented in the form of coordinates of the center point of a trapezoid. A vertical line through the centroid point divides it into two equal parts. Thus, for the height ‘h,’ the center point will be ‘h/2.’ Similarly, the other center point is calculated. These two points form the centroid. Centroid of a Trapezoid Formula is given as x = [(b+2a)/3(a+b)]h, where h is the height of the trapezoid and a and b are the length of parallel sides.

Key Terms: Trapezium, Trapezoid, Centroid, Centroid of a Trapezoid, Altitude, Quadrilateral, Parallel Sides, Base

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What is a Trapezoid?

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Trapezoid is a type of quadrilateral that has two parallel sides. It is a closed polygon with four sides. 

• A trapezoid is a two-dimensional, quadrilateral in geometry.
• The diagonals of a trapezoid intersect each other. 
• The length of the diagonals of a trapezoid is always equal. 
• The sum of the adjacent interior angles of a trapezoid is 180°
• The sum of all interior angles of a trapezoid is 360°.

Trapezoid

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Centroid of a Trapezoid

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Centroid is the center point of any geometrical object. The centroid of a trapezium is the center point of the trapezium. A vertical or horizontal line passing through the centroid of a trapezoid divides it into two halves. The representation of the centroid is in the form of coordinates. 

The coordinates of a centroid are given as 

C = [X_C, Y_C]

Where

• X_C is the point on the x-axis
• Y_C is the point on the y-axis

Read More: Quadrilaterals Important Questions

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Centroid of a Trapezoid Formula

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The centroid of a trapezoid formula is given as 

\(x = \frac{b+2a}{3(a+b)} h\)

Where

• a and b refer to the length of parallel sides.
• h is the height or altitude of the trapezoid. 

Centroid of a Trapezoid Formula

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Solved Examples on Centroid of a Trapezoid Formula

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Given below are a few examples of solved examples on Centroid of a Trapezoid Formula:

Example 1: Find the centroid of trapezoid if the dimensions are given as; a = 12 cm; b = 5 cm; h = 5 cm.

Ans. Given that,

• a = 12 cm
• b = 5 cm
• h = 5 cm

Using centroid of a trapezoid formula,

x = [(b+2a)/3(a+b)]h = [(5+2x12)/3(12+5)] x 5 

x = 2.84

Thus, the centroid of the trapezoid is 2.84 cm.

Example 2: Find the centroid of a trapezium if the parallel sides of the trapezoid measure 8 cm, 10 cm, and the height is 9 cm. 

Ans. Let us consider a and b to be the parallel sides of a trapezoid.

• a = 8 cm 
• b = 10 cm 
• h = 9 cm

Using the centroid of trapezoid formula,

x = [(b+2a)/3(a+b)]h = [(10+2 x 8)/3(8+10)] x 9

= 26/54 x 9 

= 4.33 cm

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Things to Remember

• Trapezoid is a quadrilateral, with two sides parallel to each other. 
• A trapezoid is also known as a trapezium. 
• The altitude of the trapezoid is a perpendicular line joining the two parallel sides, i.e. the bases of the trapezoid. 
• Centroid of Trapezoid refers to the center point of a trapezoid or trapezium.
• The centroid is represented in the form of coordinates like C = [X_C, Y_C].
• A line passing through the centroid divides the trapezoid into two halves. 
• The centroid of a trapezoid formula is given as x = [(b+2a)/3(a+b)]h.