Introduction
A quadrilateral is a plane closed geometric figure with four sides and four angles. A quadrilateral can be constructed using a compass and a ruler. There are several real-life examples of a quadrilateral: kites, squares, rectangles, rhombus, etc. The word quadrilateral is derived from the word “quad” which means four. Hence, there are four adjoining sides of a quadrilateral at all times.
Properties
A quadrilateral always has four sides and four angles.
The length of sides may be the same or different.
The sum of all the internal angles will be 360°.
The sum of all the external angles will also be 360°.
Construction
A quadrilateral can be constructed using a ruler and a compass if any of the following conditions are provided:
Length of four sides and one diagonal are given
Measurement of three sides and two angles are given
Measurements of two sides and three angles are given.
Types
There are a lot of examples of a quadrilateral but the most common geometric figures are square, rectangle, rhombus, parallelogram and trapezium. Except for a trapezium, all the other figures have at least two parallel sides and every quadrilateral has four vertices, four sides and four angles.
Square has all four equal sides and angles. The diagonals of a square bisect each other at 90°. Both the opposite sides of the square are parallel to each other.
Rectangle has equal opposite sides and all four equal angles. The opposite sides of a rectangle are parallel to each other as well.
Rhombus has equal sides, and opposite sides are parallel to each other. Opposite angles are equal and the sum of two adjacent angles is 180°. The diagonals from opposite sides of a rhombus bisect each other and are perpendicular to each other.
A parallelogram has two opposite and equal sides which are also parallel to each other. The opposite angles are equal and the diagonals bisect with each other.
Trapezium has only one opposite parallel and the diagonal bisectors are of the same ratio.
Quadrilaterals can be further classified as convex quadrilateral, concave quadrilateral and intersecting or crossed quadrilaterals based on the diagonals former inside a quadrilateral. In convex quadrilaterals, the diagonals are completely within the boundary of the quadrilateral while in concave quadrilaterals, the diagonals are partially outside the boundary of the quadrilateral.
Formulas
There are two basic formulas of quadrilaterals, namely: area and perimeter.
Area
Area of square: side×side
Area of rectangle: length×breadth
Area of parallelogram: base×height
Area of rhombus: ½× (first diagonal length)×(second diagonal length)
Area of trapezium: ½× (length of first diagonal)×(length of second diagonal)
Perimeter
The perimeter of square: 4×length of side
The perimeter of rectangle: 2×(length of breadth + length of a side)
Perimeter of parallelogram: 2×(base+side)
The perimeter of rhombus: 4×length of side
The perimeter of trapezium: 2×(a+b), a and b are lengths of adjacent sides.
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FAQs on Quadrilateral
1. What is a Quadrilateral? What are the Types of Quadrilaterals?
A quadrilateral is a 2-dimensional closed geometrical shape with 4 sides and 4 angles. The different types of quadrilaterals are:
Trapezium: One pair of opposite sides are parallel. All parallelograms, squares, and rectangles are trapezoids.
Parallelograms: If in a quadrilateral, both the pairs of opposite sides are parallel and equal. Opposite angles are equal.
A rectangle is a special type of parallelogram in which all the angles are equal to 900.
A square is a special type of rectangle in which all the sides are equal.
A rhombus is a parallelogram in which all sides are equal and opposites sides are parallel.
A kite is a quadrilateral in which two pairs of adjacent sides are equal and a pair of opposite angles are equal.
2. How are Problems with the Construction of Quadrilaterals Solved?
Quadrilaterals can be constructed only with the help of a ruler and compass. However, the basic knowledge of construction of angles without using a protractor is necessary. The quadrilateral has 4 sides, 4 angles, and 2 diagonals. If any of the 5 quantities among the 10 are given, the quadrilateral can be constructed. Three cases under which a quadrilateral can be constructed are:
When 4 sides and one diagonal are given
When 3 sides and 2 angles are given
When 2 sides and 3 angels are given
3. What is a concave quadrilateral?
A convex quadrilateral is a category of quadrilaterals wherein the diagonals of two sides are contained inside the boundary of the quadrilateral.
4. What is a convex quadrilateral?
A concave quadrilateral is a quadrilateral that has at least one diagonal that lies partly or entirely outside of the quadrilateral.
5. What is meant by intersecting quadrilaterals?
If in a quadrilateral, a pair of non-adjacent sides have intersecting lines, these kinds of quadrilaterals are called intersecting quadrilaterals. They are also called self-intersecting quadrilaterals or crossed quadrilaterals.
6. What are the attributes of a quadrilateral?
There are three main attributes of a quadrilateral.
There should always be four sides of a quadrilateral
There should be four vertices of a quadrilateral
The sum of all the internal angles of a quadrilateral should be equal to 360°.
7. What is the sum of internal and external angles of a quadrilateral?
The sum of all the internal angles of a quadrilateral is 360°, and the sum of all the external angles is also 360°. To learn more about quadrilaterals in detail, visit Vedantu.com.