The Ultimate Guide to Quadrilaterals: Types, Properties, and Area Formulas

Quadrilateral

A quadrilateral is a polygon with four sides

A quadrilateral is a polygon with four sides. It is a closed figure formed by connecting four line segments. Quadrilaterals come in different shapes and sizes, with each having its own unique properties.

Some common types of quadrilaterals include:
1. Square: A square is a quadrilateral with four equal sides and four right angles. The diagonals of a square are equal in length and bisect each other at right angles.
2. Rectangle: A rectangle is a quadrilateral with four right angles. It has opposite sides that are parallel and equal in length. The diagonals of a rectangle are equal in length and bisect each other.
3. Parallelogram: A parallelogram is a quadrilateral with opposite sides that are parallel. The opposite sides are also equal in length. The diagonals of a parallelogram bisect each other.
4. Trapezoid: A trapezoid is a quadrilateral with only one pair of parallel sides. The other two sides are non-parallel. The diagonals of a trapezoid do not have any specific relationships.
5. Rhombus: A rhombus is a quadrilateral with opposite sides that are parallel and equal in length. All four sides of a rhombus are equal. The diagonals of a rhombus bisect each other at right angles.

To find the area of a quadrilateral, it is important to know the type of quadrilateral and its specific properties. The formulas for calculating the area of different quadrilaterals are as follows:

1. Square: Area = side length × side length.
2. Rectangle: Area = length × width.
3. Parallelogram: Area = base length × height, where the height is the perpendicular distance between the two parallel sides.
4. Trapezoid: Area = ((sum of the lengths of the parallel sides) ÷ 2) × height, where the height is the perpendicular distance between the two parallel sides.
5. Rhombus: Area = (diagonal 1 × diagonal 2) ÷ 2, where the diagonals are the line segments connecting opposite vertices.

It is also important to note that for irregular quadrilaterals, the area can be found by dividing it into triangles or other shapes, and then calculating the areas of those individual shapes.

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