Area of Trapezoid

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The area of any object or figure can be defined as the space that the shape can occupy within itself. Similarly, the area of a trapezoid can be defined as the number of units ( square ) which can be fitted in the trapezoid. For example, let us assume that the length of 15 square units is equivalent to 1 cm, this signifies that the area of trapezoid is = 15 cm square units. The formula given to calculate the area of a trapezoid is: ½ * a + b * h where ‘a’ and ‘b’ is denoted as the bases of the trapezoid and ‘h’ is considered as the height of the trapezoid. In this article, we shall discuss some interesting topics such as: what is a trapezoid, some examples based on the area of a trapezoid, and do a detailed discussion about those topics. 

What is a Trapezoid? 

In mathematics, there are various types of shapes that are divided into types: two-dimensional shapes and three-dimensional shapes. One of type two-dimensional shape is a trapezoid. It is considered to be a quadrilateral which consists of both the parallel and nonparallel sides. It can also be defined as a polygon that comprises only one pair of sides which are parallel. A trapezoid can be regarded as a shape that has four sides. Therefore, it has its own perimeter and area. The parallel sides of a trapezoid are also known as the bases of trapezoids. Similarly, the non-parallel sides are mostly referred to as the legs of the trapezoid. 

Some Important Properties of a Trapezoid 

Like any other geometric shape in mathematics, a trapezoid also possesses its own properties which makes it different from other geometric shapes. Some of the properties are listed below: 

  • The angles, bases, and sides of an isosceles trapezoid are congruent or equal to each other. 
  • The point of intersection will be collinear to the midpoints of the given two sides. 
  • The perimeter of the trapezoid is the sum of all four sides. For example, a + b + c +d. 

Some Examples Based on the Area of Trapezoid 

As mentioned above, the mathematical formula to calculate the area of a trapezoid is: ½ * a + b * h where ‘a’ and ‘b’ is denoted as the bases of the trapezoid and ‘h’ is considered as the height of the trapezoid. To excel in any topic of mathematics, one must solve various examples related to it. The examples related to the area of a trapezoid are listed below: 

Example 1: Calculate the area of the trapezoid if the bases and heights are: 15 cm and 5 cm and 3 cm respectively? 

Solution: Given that, 

Bases of the trapezoid are: 15 and 5 cm respectively 

Height of trapezoid is : 3 cm 

Using the formula of the area of trapezoid: ½ * a + b * h . 

½ * ( 15 + 3 ) * 3 = ½ * ( 18 ) * 3 

 ½ * ( 18 ) * 3 = 1 * 9 * 3 

1 * 9 * 3 = 27 cm square units. 

Hence, the area of a trapezoid for the given bases and height is equivalent to 27 cm square units. 

Example 2: Find the area of the trapezoid if the bases and heights are: 16 cm and 8 cm and 3 cm respectively? 

Solution: Given that, 

Bases of the trapezoid are: 16 and 8 cm respectively 

Height of trapezoid is : 3 cm 

Using the formula of the area of trapezoid: ½ * a + b * h . 

½ * ( 16 + 8 ) * 3 = ½ * ( 24 ) * 3 

 ½ * ( 24 ) * 3 = 1 * 12 * 3 

1 * 12 * 3 = 36 cm square units. 

Thus, the area of trapezoid for the given bases and height is equivalent to 36 cm square units. 

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