What is a trapezium? It would be a couple of two parallel sides where the length is unequal and both the sides would be non-parallel. The parallel side of a trapezium would be called bases as the non – parallel sides of a trapezium are termed as legs. It is also known as a trapezoid.
Let us take the example of a trapezium ABCD. The bases would be AB and CD that would be parallel to each other. AD and BC are legs that are non-parallel sides. The two diagonals are AC along with BD whereas AE would be the distance between the two parallel sides as it would be the height of the trapezium ABCD
The shape of a trapezium
In different countries, the shape of the trapezium is known to vary. A lot would be dependent upon the sides of a trapezium there is bound to be confusion about the terms trapezium and trapezoid. Since the meaning of both the two words is in British and the US, then the definition would be exactly reversed.
In the US, a trapezium would be defined as a quadrilateral where there are no parallel sides. Coming to a trapezoid is a quadrilateral where one pair of parallel sides are equal. In Britain, a trapezium would be a quadrilateral where one pair of parallel sides exists, and a trapezoid would be a quadrilateral with no parallel sides.
Trapezium and their types
A trapezium is split into three categories that are discussed below
- Isosceles trapezium- it is a form of a trapezium, where both angles and both base angles would be of the same measure.
- Right trapezium- it is a form of a trapezium having a couple of right angles.
- Scalene trapezium- it is a form of a trapezium with no sides or angles equal
The properties of a trapezium
Hereby are a few properties of a trapezium
- A pair of opposite sides would be parallel
- Both the diagonals intersect each other
- A couple of non-parallel sides would be unequal except for an isosceles triangle
- A couple of adjacent pairs of angles would be adding up to 180 degrees
- The line that would be joining the mid-points of the non-parallel sides would be always parallel to the bases. Even the parallel sides would be equal to the sum of the parallel sides.
- The sum of the four interior angles is 4 right angles, that is 360 degrees
- Now the sum of the four exterior angles is 4 right angles which are 360 degrees
The area of trapezium would be ½ which is( sum of the parallel sides) and the distance between them. Here a and b would be the bases where h is the altitude to the distance or height between them.
The perimeter of a trapezium
The perimeter of a trapezium would be the sum of all four sides. In mathematical terms the perimeter arrives at AB+ BC+ AD + CD) where all of them would be the four sides of a trapezium.
The diagonals of a trapezium would not bisect each other. If by any chance they would be bisecting it is a parallelogram. So every parallelogram is a trapezium but every trapezium may not be a parallelogram always.
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