What is the formula to find the area of a trapezium?

What is the formula to find the area of a trapezium?

In the field of geometry, there are various geometrical figures that we often use for the calculation purpose. These figures help us understand the configuration of the different calculations as well.

In the common termstrapezium is a quadrilateral, that is to be defined as a shape with four sides and there is also one set of parallel sides. Apart from trapezium, we will always come across different types of quadrilateral as well so we will be able to have a communication for that as well.

1. Parallelogram
2. Rectangle
3. Square
4. Rhombus

In all of the above quadrilaterals that we will deal with they all will have one common property, which is, the sum of all the angles is 360°.

1. In the figure the  pair of parallel sides are called the bases and on the other hand  the non-parallel sides are called the legs of the trapezoid
2. In the figure the line segment that connects  the midpoints of the non-parallel sides of a trapezoid is known as the  mid-segment
3. In the trapezium the parallel sides will be representing the different ways in which the representation can be done as well in a coordinated manner.
4. Here when we draw a line segment, that lies between the two non-parallel sides, where we will be able to connect the mid-point of both sides, then the trapezium will be divided into two unequal parts.
5. Here we can also take the case of the isosceles triangles, where the two sides of a triangle are equal and the angle that are opposite to the equal sides are also equal. In the similar manner, when we are to come across a similar  type of a figure we get the  Isosceles Trapezium, where the two non-parallel sides are equal and  then they form equal angles at one of the bases.

AREA OF TRAPEZIUM

Area of trapeziumcan be calculated by using the below formula:

• Area = (1/2) h (AB+CD)

When we are speaking about the area of the trapezium that is termed as the region covered by a trapezium in a two-dimensional plane. It is called to be the space that is enclosed in 2D geometry. In the similar manner we will come across many other geometrical shapes thatwill alsohave its own properties and formulas based on area and perimeter.

Derivation of Area of a Trapezium

There are various steps that are being followed that will help us understand the derivation of the area of trapezium. Here this is important to understand that the area of a trapezoid is equal to the sum of the areas of the two triangles and also the area of the rectangle.

 The fact that we know,

Area of trapezoid = area of triangle 1 + area of rectangle + area of triangle 2.

This can be represented as:

A = (ah/2) + b₁h + (ch/2)
A = (ah + 2b₁h + ch)/2

so, here we will simplify the  equation,  and then rearranging the terms, and when we apply  factoring result to:
A = h/2[b₁ + (a + b₁ + c)] ….(i)
let us assume here that we assume the longer base of the trapezoid be b₂, then
b₂ = a + b₁ + c …..(ii)
here, we will sunbstitute, (ii) in equation (i),
A = h/2(b₁ + b₂)

Therefore,  when we calculate the  area of a trapezoid with bases b₁, b₂ and altitude h is;

A = h/2(b₁+b₂)

Properties of a Trapezium

The trapezium is one of the most important geometrical figures that we often come across. There are different calculations that are being done based on the representations on the sides as well. So this is so very important that we should be able to learn about the different properties of the trapezium.

1. The properties of the trapezium remain the same just like the other quadrilateral where the sum of all the four angles of the trapezium is equal to 360°
2.  The geometrical figure of the trapezium will have two parallel sides and two non-parallel sides
3. When we draw the diagonals in the geometrical figure, the diagonals of regular trapezium will always bisect each other
4. If we calculate the length of the mid-segment of the trapezium then it is equal to half the sum of the parallel bases.
5.  The two pairs of adjacent angles of a trapezium that areformed between the parallel sides and the other that is formed to one of the non-parallel side, add up to 180 degrees

APPLICATION

This is one of the concepts that are highly used in a number ofphysics computations and other mathematical calculations. This also acts as the basis for obtaining the equations of motion. This is also one of the figures that will help us understand the orientation of the figure as well.