Parallelogram, Trapezium and Kite

Some people may find parallelogram, trapezium and kite similar, but they are not. All these are quadrilateral, have four sides, four vertices, four angles, and have the sum of interior angles equal to 360 degrees. However, they have different sizes and properties. So let us study about them.

Parallelogram

A parallelogram is a quadrilateral with two sets of parallel sides.

Properties of a parallelogram

1. The sides of a parallelogram are equal in length and parallel to each other.
2. The opposite angles inside a parallelogram are equal in value.
3. The sum of adjacent sides in a parallelogram is equal to 180 degrees.
4. The consecutive angles of a parallelogram are supplementary.
5. The diagonals of a regular parallelogram bisect each other, i.e., they form 90 degrees at the meeting junction.
6. Each diagonal of a parallelogram divides the entire parallelogram into two congruent triangles.
7. The two diagonals divide the entire parallelogram into four congruent triangles.
8. Square, rectangle and rhombus are particular types of a parallelogram.
9. Area of parallelogram = base x height.

Trapezium

A trapezium is a quadrilateral whose one pair of opposite sides are parallel. The parallel bottom side is the base, while its non-parallel side is the legs. Thus, it is also known as a trapezoid.

Properties of a trapezium

1. The parallel sides are equal in a trapezium.
2. In an isosceles trapezium, the two non-parallel sides are equal. They also form equal angles with the bases.
3. The diagonals of a trapezium intersect each other. In addition, they do not bisect each other.
4. The sum of interior angles in a trapezium is equal to 360 degrees.
5. The sum of adjacent angles in a trapezium is equal to 180 degrees. This implies the adjacent angles in a trapezium are supplementary.
6. There are three types of trapezium – isosceles, scalene and right trapezium.
7. In a scalene trapezium, all the sides are of unequal length.
8. In a right trapezium, it forms two right angles.

Kite

A kite is a closed quadrilateral that has two pairs of adjacent sides of equal length. It is a plane figure with adjacent sides congruent.

Properties of a kite

1. The two angles in a kite, where the unequal sides meet, are equal.
2. A kite can be assumed as a pair of two congruent triangles with a common base.
3. The two diagonals in a kite intersect each other at right angles.
4. The sum of interior angles in a trapezium is equal to 360 degrees.
5. A regular kite is symmetrical about its main diagonal.
6. The shorter diagonal in a kite divides the entire kite into two isosceles triangles.

Example 1: Find the perimeter of a kite whose sides are 5 cm and 6 cm.

Solution: The sum of sides of a quadrilateral is equal to the perimeter. Also, the two pairs of sides are equal in length in a kite. Therefore, the perimeter of the kite is 5 + 5 + 6 + 6 = 22 cm.

Example 2: Find the area of a parallelogram whose base is 4 m and height is 10 m.

Solution: We know, the area of a parallelogram = base x height Therefore, area of parallelogram = 4 x 10 = 40 square meters.