 # Quadrilaterals

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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. Quadrilaterals

### 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. POST A NEW COMMENT