A trapezoid also known as a trapezium is a four-sided polygon or a quadrilateral. It has one set of opposite sides which are parallel and a set of non-parallel sides. The parallel sides are known as the bases and the non-parallel sides are known as the legs of the trapezoid.
There are different types of trapezoids: isosceles trapezoid, right trapezoid, and scalene trapezoid.
A trapezoid with the two non-parallel sides of the same length is called an isosceles trapezoid.
A right trapezoid is a trapezoid that has at least two right angles.
A right isosceles trapezoid is a trapezoid that is simultaneously a right trapezoid and an isosceles trapezoid. In Euclidean geometry, such trapezoids are automatically rectangles.
Let's look into the Trapezoid formulas in detail.
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The perimeter of a trapezoid is defined as the sum of all its sides or the complete boundary of the trapezoid. Consider a trapezoid ABCD as shown below with side measures a,b,c, and d. Let's look into the Trapezoid Formula
The perimeter of the trapezoid is calculated by finding the sum of all the sides i.e, AB + BC + CD + DA
Perimeter of a Trapezoid = Sum of all the sides = a + b + c + d
Formula to Calculate Area of a Trapezoid
The area is defined as the area or region occupied by the trapezoid. Consider a trapezoid ABCD as shown below.
The area of a trapezoid is given by:
Area of a Trapezoid = (1/2) × h × (a + b)
a = Shorter base
b = Longer base
h = Distance or height between the two bases
Let us see the applications of the trapezoid formula in the following solved examples.
Solved Examples Using Trapezoid Formula
Example 1: If the perimeter of a trapezoid is 60 cm and three of its sides are 15 cm, 20 cm, and 16 cm respectively, find the measure of the fourth side using Trapezoid Formula.
Given: Perimeter = 60 cm, a = 15 cm, b = 20 cm, c = 16 cm, d = ?
We know that, according to Trapezoid Formula,
Perimeter of a trapezoid = Sum of all the sides
⇒ a + b + c + d = 60
⇒ 15 + 20 + 16 + d = 60
⇒ d = 9 cm
Answer: Thus, the fourth side measures 9 cm.
Example 2: Find the area of a trapezoid whose bases are 19 cm and 15 cm and height is 8 cm.
a = 17 cm
b = 19 cm
h = 8 cm
We know that, according to trapezoid formula,
Area of a trapezoid = h(a+ b) / 2
= 8 (15 + 19) / 2
= 4 × 34
= 136 cm2
Answer: Thus, the area of the trapezoid is 136 cm2