What is the Area of a Trapezoid Formula?
A trapezoid is a quadrilateral that is covered in the Mensuration segment of mathematics. In Mensuration, we learn how to find the area, perimeter, and volume of various closed plane figures and solid figures, such as circles, triangles, rectangles, trapezium, cube, cuboids, and cylinders, etc. In this article, we will know the methods of finding the area of a trapezium or trapezoid. Now, before that, let us recapitulate - What is Area? - The measurement of the part of an enclosed plane within a rectilinear figure is called its area.
What is a Trapezoid?
A trapezoid or trapezium is a quadrilateral- a two-dimensional geometrical figure with one pair of parallel sides. It is a four-sided polygon, a plane figure with a closed shape. A trapezoid has four line segments and four interior angles. The parallel sides of a trapezoid are called the bases and the other non-parallel sides are called legs. So, there are two bases and two legs in a trapezoid. The height of a trapezoid is the perpendicular line from one base to the other base (i.e. to the other parallel side). A line that joins the midpoints of the two legs is the median of a trapezoid. In an isosceles trapezoid, the diagonal bisects each other.
Area of Trapezium Formula
The area of a trapezoid is equal to half the sum of parallel sides that is multiplied by the height from the base to the other base. To understand the area of a trapezoid formula, let’s first look at the following figure:
Therefore, the trapezoid formula is:
Area = ½ × (Sum of parallel sides) × height = ½ × (AB + CD) × MD
Therefore, if height = 0.
The area of trapezium without height will be zero!
Example 1:
The area of a trapezium is 450m2, the distance between two parallel sides is 10 m, and one of the parallel sides 15 m. Find the other parallel side.
Solution:
Given, one of the parallel sides of the trapezium, a = 15m
Its height (h) = 10m
Let another side be m and then, area of the trapezoid = 450m2
Area of trapezium formula = ½ [h(a + b)]
⇒ 450 = ½ × 10 × (15 + b) ⇒ (450 × 2)/10 = 15 + b ⇒ 90 = 15 + b
∴ b = 90 - 15 = 75
Hence, the other parallel side of the trapezoid is 75m.
Example 2:
Find the Area of Trapezium: ABCD is an isosceles trapezoid where AB = AD = DC = 8 cm and BC = 16 cm. Calculate the area of isosceles trapezium.
An isosceles triangle has one pair of non-parallel sides congruent.
Area of trapezium formula = ½ × (sum of parallel sides) × height
= (a + b)/2 × h
= (8 + 16)/2 × √(48)
= 12 × √(48)
= 83.14 sq. cm
[Now, to find h, we have to apply Pythagorus Theorem:
(Image will be uploaded soon)
c2 = a2 + b2
82 = h2 + 42
64 = h2 + 16
64 - 16 = h2
48 = h2
∴ h = √(48)]
The trapezium is an important planar structure. Examples of trapezoid shapes in daily life can be found in handbags, popcorn tins, musical instruments like guitar, etc. There are many other applications of the area of a trapezoid formula.
FAQs on Area of a Trapezoid Formula
1. What are the Properties of a Trapezoid?
Ans: The trapezoidal rule formula for area is based on the following properties:
A trapezoid is a quadrilateral with not more than one pair of parallel sides.
The parallel sides of a trapezoid are called the bases of the quadrilateral.
The base angles of a trapezoid are the pairs of angles that have a common base.
A scalene trapezoid is a closed quadrilateral figure with no parallel sides.
An isosceles trapezoid is a trapezoid in which two non-parallel sides are equal and congruent.
There are two bones in your wrist called trapezoids because they are in the shape of this quadrilateral.
2. What are the Properties of a Scalene Trapezoid?
Ans: A scalene trapezoid has the following properties:
It has four sides of unequal length.
The two bases are parallel but of different lengths.
The two legs are of different lengths.
3. What is an Isosceles Trapezoid and What are its Properties?
Ans: If the legs of a trapezoid are equal and congruent, the trapezoid is called isosceles. The properties of an isosceles trapezoid are:
A quadrilateral is an isosceles trapezoid if and only if the legs are equal.
A quadrilateral is an isosceles trapezoid if and only if the diagonals are congruent.
A quadrilateral is an isosceles trapezoid if and only if its opposite angles are supplementary (i.e. the sum of the two angles is 180 degrees).
