Trapezoid and How Important It Is In The Domain of Maths

A trapezoid is a quadrilateral that has four parallel sides. In some parts of the world it is known as trapezium. This happens to be a four sided figure or shape that would cover some area and have a perimeter. It happens to be a 2 d figure and not a 3d figure. The sides that are parallel to each other are termed as bases of the trapezoid. Coming to the non- parallel sides it is known as the lateral sides or legs. Any form of distance between both the parallel sides is referred to as the altitude. The area of trapezoid is a point to consider.

Till this point of time there is a disagreement about the definition of trapezoid. A school of Maths does consider it as having one and only pair of parallel sides. Others would argue that could be more than one pair of parallel sides in a trapezoid. If we take the second definition a parallelogram is a trapezoid based on the inputs available. Though some experts do not consider a parallelogram to be a trapezoid. One thing that emerges it is already a pair of quadrilateral.

The types of trapezoids

The classification of trapezoids takes place in three groups. They are as follows

  • Right trapezoid- such a type of trapezoid would be having a pair of right angles
  • Isosceles trapezoid- if there are non- parallel sides then the legs of a trapezoid would be equal in length. It is known as an isosceles trapezoid.
  • Scalene trapezium- it is a type of trapezoid where neither the sides or the angles would be equal

The shape of a trapezoid

As already discussed a trapezoid is a four shaped figure where one of the sides would be parallel. It occurs to be a two dimensional figure as it would be similar to square, rectangle or parallelogram. Hence this shape would also have an area along with a perimeter just like other shapes do. Once you are aware about the formula for the perimeter and area the task may become an easy one.

The perimeter and area of a trapezoid

Coming to the area of a trapezoid, it may be calculated as an average of both bases and then you would multiply it with the altitude. The formula of calculating

Area = ½( a+b) h

The perimeter of a trapezoid would be a sum of all the four sides. If a trapezoid has sides a, b, c and d then the formula of the trapezoid would be

Perimeter= a+ b+c+ d

For example the four sides would be measuring 3m, 5m,7m and 9 m. Since we are aware that perimeter would be the sum of all the four sides , So the perimeter in this case would be 26 m.

Properties of trapezoid

Below are mentioned some of the properties of a trapezoid

  • The diagonals and base angles of an isosceles trapezoid is equal
  • If you are drawing a median on a trapezoid, it would be parallel to the bases as the length is going to be an average of the bases
  • An intersection point of the diagonals would be collinear to the points which is the midpoint of both of them.
  • If a trapezoid has three sides a, b and c, with the diagonals p and q then the equation would be

p2+q2= c2+d2+2ab

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