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Answers
Answer:
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Explanation:
Quadrilateral Definition
A quadrilateral is a plane figure that has four sides or edges, and also have four corners or vertices. Quadrilaterals will typically be of standard shapes with four sides like rectangle, square, trapezoid, and kite or irregular and uncharacterized as shown below:
Types of Quadrilaterals
There are many types of quadrilaterals. As the word ‘Quad’ means four, all these types of a quadrilateral have four sides, and the sum of angles of these shapes is 360 degrees.
Trapezium
Parallelogram
Squares
Rectangle
Rhombus
Kite
Quadrilateral Formula
The area of the quadrilateral is the total space occupied by the figure. The area formula for the different quadrilaterals are given below:
Area of a Parallelogram Base x Height
Area of a Rectangle Length x Width
Area of a Square Side x Side
Area of a Rhombus (1/2) x Diagonal 1 x Diagonal 2
Area of a Kite 1/2 x Diagonal 1 x Diagonal 2
Perimeter of Quadrilateral
Perimeter is the total distance covered by the boundary of a 2d shape. Since we know the quadrilateral has four sides, therefore, the perimeter of any quadrilateral will be equal to the sum of the length of all four sides. If ABCD is a quadrilateral then, the perimeter of ABCD is:
Perimeter = AB + BC + CD + AD
Quadrilateral Name Perimeter
Square 4 x Side
Rectangle 2(Length + Breadth)
Parallelogram 2(Base + Side)
Rhombus 4 x Side
Kite 2 (a + b), a and b are adjacent pairs
Quadrilateral Properties
Let us understand in a better way with the help of an example:
Quadrilateral
Four sides: AB, BC, CD, and DA
Four vertices: Points A, B, C, and D
Four angles: ∠ABC, ∠BCD, ∠CDA, and ∠DAB
∠A and ∠B are adjacent angles
∠A and ∠C are the opposite angles
AB and CD are the opposite sides
AB and BC are the adjacent sides
A quadrilateral is a 4-sided plane figure. Below are some important properties of quadrilaterals :
Every quadrilateral has 4 vertices, 4 angles, and 4 sides
The total of its interior angles = 360 degrees
Square Properties
All the sides of the square are of equal measure
The sides are parallel to each other
All the interior angles of a square are at 90 degrees (i.e., right angle)
The diagonals of a square perpendicular bisect each other
Rectangle Properties
The opposite sides of a rectangle are of equal length
The opposite sides are parallel to each other
All the interior angles of a rectangle are at 90 degrees.
The diagonals of a rectangle bisect each other.
Rhombus Properties
All the four sides of a rhombus are of the same measure
The opposite sides of the rhombus are parallel to each other
The opposite angles are of the same measure
The sum of any two adjacent angles of a rhombus is equal to 180 degrees
The diagonals perpendicularly bisect each other
Parallelogram Properties
The opposite side of the parallelogram are of the same length
The opposite sides are parallel to each other
The diagonals of a parallelogram bisect each other
The opposite angles are of equal measure
The sum of two adjacent angles of a parallelogram is equal to 180 degrees
Properties of Trapezium
Only one pair of the opposite side of a trapezium is parallel to each other
The two adjacent sides of a trapezium are supplementary (180 degrees)
The diagonals of a trapezium bisect each other in the same ratio
Properties of Kite
The pair of adjacent sides of a kite are of the same length
The largest diagonal of a kite bisect the smallest diagonal
Only one pair of opposite angles are of the same measure.
Summary of Quadrilateral Properties
Square Rectangle Rhombus Parallelogram Trapezium
All sides are equal Yes No Yes No No
Opposite sides are parallel Yes Yes Yes Yes Yes
Opposite sides are equal Yes Yes Yes Yes No
All the angles are of the same measure Yes Yes No No No
Opposite angles are of equal measure Yes Yes Yes Yes No
Diagonals bisect each other Yes Yes Yes Yes No
Two adjacent angles are supplementary Yes Yes Yes Yes No
Quadrilaterals and its properties
Notes on Quadrilateral
A quadrilateral is a trapezoid or a trapezium if 2 of its sides parallel to each other.
A quadrilateral is a parallelogram if 2 pairs of sides parallel to each other.
Squares and Rectangles are special types of parallelograms. Below are some special properties.– All internal angles are of “right angle” (90 degrees).– Each figure contains 4 right angles.– Sides of a square are of the same length (all sides are congruent) – Opposite sides of a rectangle are same.– Opposite sides of a rectangle and square are parallel.
A quadrilateral is a rhombus, if
All the sides are of equal length-Specified 2 pairs of sides are parallel to each other.
A kite is a special sort of quadrilateral, in which 2 pairs of adjacent sides are equal to each other.
Quadrilaterals Solved Example
Example 1: What is the base of a rhombus, if its area is 40 square units and the height is 8 units?
Solution:
Given,
Area = 40 square units
Height = 8 units
Area of rhombus = Base × Height
40 = Base × 8
Base = 40/8 = 5 units