Quadrilateral
The word “Quadrilateral” is taken from the two different words of the Latin language in which “Quadri” means four and lateral means sides, showcasing the fact that it has four sides. The interesting fact about a quadrilateral is that it includes a wide range of different shapes with various properties and not necessarily with all equal sides.
1.0Quadrilateral Definition in Mathematics
The Quadrilateral is a two-dimensional geometric polygon with four sides, vertices, and four angles. The quadrilateral is constructed by joining the set of four points, for instance, A, B, C, and D, in a two-dimensional plane forming the sides AB, BC, CD, and DA and angles ∠A, ∠B, ∠C, and ∠D.
The diagonals of the quadrilateral are formed by joining the opposite vertices; in quadrilateral ABCD, the diagonals are AC and BD.
2.0Properties of Quadrilaterals
The properties of quadrilaterals differ with different shapes of the quadrilaterals, that is, rectangle, square, trapezium, etc. Here are some general properties of a quadrilateral, which remain constant for every quadrilateral shape:
- All quadrilaterals have four sides, four vertices, and four angles.
- The sum of the interior angles of any quadrilateral is always equal to 360°.
- All the quadrilaterals have only two diagonals connecting the opposite side of the quadrilaterals.
- Quadrilaterals with all the interior angles less than 180° are known as the convex quadrilaterals. On the other hand, quadrilaterals with at least one interior angle greater than 180° are called concave quadrilaterals.
- The sum of all the exterior angles of any quadrilateral is also equal to 360°.
3.0Quadrilateral Types
Quadrilaterals, based on different properties and shapes, are divided into different types of quadrilaterals. Which includes:
4.0Formulas Related to Quadrilaterals
The two types of basic formulas of quadrilaterals include the Area and Perimeter of all the quadrilaterals. The Formula for each which are:
5.0Solved Problems
Problem 1: A rectangular garden having a length of 15m and a width of 10m. The gardener wants to lay out grass over the entire garden. How much area does he need to cover with grass?
Solution: According to question length = 15m and breadth = 10m
Area of rectangular garden =
=
Hence, the Area he needs to cover with grass is 150m2
Problem 2: In a trapezium, the lengths of the parallel sides are 10 cm and 14 cm. The distance between the parallel sides (height) is 8 cm. Find the area of the trapezium.
Solution: According to the question
length of the parallel side (1) let a = 10cm
length of the parallel side (2) let b = 14cm
Height between parallel sides = 8cm
The Area of the Trapezium =
=
Problem 3: A rhombus has one diagonal that is 12 cm longer than the other. The area of the rhombus is 144 cm². Find the lengths of both diagonals.
Solution: According to the question,
The area of the rhombus = 144 cm2