A quadrilateral is any closed shape that has four sides. The sum of the measures of the angles is 360o. Some of the known quadrilaterals are square,rectangle, trapezium, parallelogram and rhombus.

### Square

A square is a regular quadrilateral that has four right angles and parallel lines. The diagonals also bisect each other perpendicularly.

Properties

If the side of the square is a, then its

• Perimeter = 4a
• Area = a2
• Length of the diagonal = √2a

### Parallelogram

A parallelogram is a quadrilateral in which opposite sides are equal and parallel. Any two opposite sides of a parallelogram are called bases, a distance between them is called a height.

Properties

• Area of a parallelogram = base x height
• Perimeter = 2(Sum of two consecutive sides)
• Opposite sides of a parallelogram are equal
• Opposite angles of a parallelogram are equal
• Diagonals of a parallelogram are divided in their intersection point into two.
• The sum of square of diagonals is equal to the sum of squares of four sides  AC2+BD2=AB2+BC2+CD2+AD2

### Rectangle

A rectangle is a parallelogram with all its angles equal to right angles.

Properties

• Sides of the rectangle are its heights simultaneously.
• Diagonals of a rectangle are equal: AC = BD.
• Area of diagonals = length x breadth

### Rhombus

If all sides of a parallelogram are equal, then this parallelogram is called a rhombus.

Properties

• Diagonals of a rhombus are mutually perpendicular and divide its angles into two.
• Area of a rhombus is given by

### Trapezoid

A trapezium

A trapezoid is a quadrangle two opposite sides of which are parallel.

Here AD||BC, parallel sides are called bases of a trapezoid, the two others(AB and CD) are called lateral sides. A distance between bases(BM) is a height. The segment EF, joining midpoints E and F of the lateral sides, is called a midline of a trapezoid. A midline of a trapezoid is equal to half the sum of bases.

If AB = CD, the trapezoid is called an isosceles trapezoid.

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