A trapezoid is considered to be a fascinating study all over the world. A trapezoid is also considered a trapezium. It is an important topic included in geometry.
It is considered to be a four-sided figure. It is a closed figure. It has an area and a perimeter. It has two sides that are parallel to each other, known as bases. The nonparallel sides of the trapezoid are known as lateral sides. The sides that are not parallel are called as legs of the trapezoid. The shortest distance between the two parallel sides is known as the altitude of the trapezoid.
Few properties of trapezoid are listed below
- It has two opposite sides that are parallel to each other are known as bases.
- If the opposite sides have the same length then it is known as an isosceles trapezoid.
- In a trapezoid angles next to each other has a total of 180 degrees.
- The median is parallel to both the parallel bases.
- The length of the median is the average of both the parallel bases. (A+ b) \2
- If both the pairs of parallel opposite sides of a parallelogram are not equal then it is a scalene trapezoid.
- If both the pairs of parallel opposite sides are of equal length and at a right angle to each other then the trapezoid is a square.
- Both the pairs of opposite parallel sides and their opposite sides are of equal length then it is a rectangle trapezoid.
There are three types of a trapezoid-
- Scalene trapezoid
- Isosceles trapezoid
- Right trapezoid
- In the Isosceles trapezoid the nonparallel sides, known as legs of a trapezoid are equal in length. In Isosceles trapezoid angles of parallel sides that are known as a base are equal. There is a line of symmetry in the isosceles trapezoid. The diagonals in isosceles trapezoid are equal in length.
- In scalene trapezoid neither the angle, nor the sides are equal.
- In the right trapezoid the pair of sides is at right angle to each other. Right-angled trapezoid is used to measure the estimated area under a curve.
The area of trapezoid is defined as the sum of parallel sides that are known as bases / 2 multiplied by the height of the trapezoid. (AB + CD/2) X height of trapezoid.
The perimeter of a trapezoid is defined as the total of all the sides.
In a trapezium 4 sides of the polygon are equal but one pair of opposite sides are parallel to each other. A quadrilateral is said to be a trapezium if adjacent angles sum up to 180 degrees then are they are supplementary. The angle between the side and the diagonal is equal to the angle between the opposite sides and the same diagonal. The diagonals intersect each other in the same ratio. Diagonals cut a quadrilateral into four triangles where opposite pair have an equal area.
The study of a trapezoid is very useful in the following fields-
Cuemath is an online math learning program that helps to work upon the formulas in Arithmetic. It is one class where is student is helped by a teacher to gain mastery in Arithmetic.
The trapezoid has a two-dimensional shape. It has four vertices and edges. It has no line of symmetry. In real life top of the table, a handbag, roof of the house, and a pencil box is the example of a trapezoid. A trapezoid is not a parallelogram as the parallelogram has opposite sides parallel whereas in trapezoid only the bases are parallel to each other. A quadrilateral can be a trapezoid. The difference between trapezium and trapezoid is still controversial. A four-sided polygon having a closed figure is known as a trapezoid. In architecture the word trapezoid represents the doors and windows that are symmetrical.