Area Of A Trapezoid Formula

Trapezoid formula

In geometry, a trapezium is a quadrilateral with one pair of parallel sides (called bases) and one pair of non-parallel sides (called legs). The area of a trapezium is the number of unit squares that can fit inside it. It is often measured in square units like cm2, m2, and so forth. In this post, we will look at the area of a trapezium formula and several instances.

Area of Trapezoid Formula

The area is defined as the area or region that the trapezium occupies. It is equal to half of the total of its bases multiplied by their distance. The area of a trapezium is given as:

Area of a Trapezoid  = (1/2) × h × (a + b)

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where,

  • a = Shorter base
  • b = Longer base
  • h = Height or distance between the two bases

Examples on Area of Trapezoid

Example 1: Calculate the area of a trapezoid whose parallel sides are 22 cm and 12 cm, respectively, and whose height is 6 cm.

Solution: The bases are given as, a = 22 cm; b = 12 cm; the height is h = 6 cm.

The area of the trapezoid = A = ½ (a + b) h

A = ½ (22 + 12) × (6) = (34) × (3) = 102 cm2.

Example 2: Calculate the height of the trapezoid, if the sum of the parallel sides is 30 m and the area is 60 m2.

Solution:

Given: a+b = 30 m

Area, A = 60 m2.

To find: h

We know that the formula for area of trapezoid, A = (½) [(a+b)h] square units

Substituting the values in the formula, we get

60 = (½)[30h]

60/30 = (½)h

2 = h/2

h = 4.

Therefore, the height of the trapezoid is 4 m.

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FAQs (Frequently Asked Questions)

1. What is Area of Trapezoid in Math?

A trapezoid’s area is equal to the number of unit squares it can accommodate. A trapezium is defined as a four-sided quadrilateral with one set of opposing sides parallel. The formula for calculating the area of a trapezoid is ½ (a + b) h, where ‘a’ and ‘b’ are the bases (parallel sides) and ‘h’ is the perpendicular height. It is expressed as square units.

2. How to Find the Area of a Trapezoid?

The area of a trapezoid is found using the formula, A = ½ (a + b) h, where ‘a’ and ‘b’ are the bases (parallel sides) and ‘h’ is the height (the perpendicular distance between the bases) of the trapezoid.

3. Is trapezium and trapezoid the same?

A trapezoid and a trapezium are actually the same shape