GRE Geometry | Quadrilaterals

A quadrilateral is a 2 – D shape which contain 4 sides. It consist of four sides, four angles and four vertices.

Different type of quadrilateral and their properties:

  1. Rectangle:
    The rectangle, like the square, is one of the most commonly known quadrilaterals. It is defined as having all four interior angles 90° (right angles).



    • All four angles in a rectangle are 90°.
    • Opposite side are parallel and of same length(or congruent).
    • Diagonals of rectangle bisect each other and divide a the rectangle into two congruent triangles.
    • Area of rectangle = length * breadth.
    • Perimeter of rectangle = 2*(length + breadth)


  2. Square:
    In geometry, a square is a regular quadrilateral, which means that it has four equal sides and four equal angles (90-degree angles, or (100-gradian angles or right angles). It can also be defined as a rectangle in which two adjacent sides have equal length.

    • All four angles in a rectangle are 90°.
    • All sides are equal and opposite sides are parallel(or congruent).
    • Diagonals of square bisect each other at 90° and divide the square into two congruent triangle.
    • Area of square = side * side
    • Perimeter of square = 4 * side


  3. Rhombus:
    A Rhombus is a flat shape with 4 equal straight sides. A rhombus looks like a diamond. All sides have equal length. Opposite sides are parallel, and opposite angles are equal (it is a Parallelogram).

    • All sides are equal in a rhombus.
    • Opposite angles are equal in rhombus.
    • The diagonals of rhombus intersect each other at equal angles.
    • Area of rhombus = (diagonal1 * diagonal2) / 2
    • Perimeter of rhombus = 4 * side


  4. Trapezium:
    In Euclidean geometry, a convex quadrilateral with at least one pair of parallel sides is referred to as a trapezoid.


    • Atleast one pair of opposite side is parallel to each other.
    • Area of trapezium = (sum of length of parallel side(or bases)) * height / 2.
    • Perimeter of trapezium = sum of all sides.


  5. Parallelogram:
    In Euclidean geometry, a parallelogram is a simple quadrilateral with two pairs of parallel sides. The opposite or facing sides of a parallelogram are of equal length and the opposite angles of a parallelogram are of equal measure.

    • Opposite sides are parallel and congurent to each other.
    • Opposite angles are congurent to each other.
    • Sum of adjacent angles is 180°
    • Diagonals of parallelogram bisect each other and divide the parallelogram into two congurent triangles.
    • Area of parallelogram = length * breadth
    • Perimeter of parallelogram = 2(length + breadth)

Some examples on quadrilateral:
What will be the area and perimeter of given rectangle if length of rectangle is 5cm and breadth of rectangle is 7cm?

Solution:

Area of rectangle = length * breadth. 
Area of rectangle = 5 * 7 = 35 cm2
Perimeter of rectangle = 2*(length + breadth)
Perimeter of rectangle = 2*(5 + 7) = 24cm

What will be the are of given rhombus if diagonal of rhombus are 4cm and 6cm?

Area of rhombus = (diagonal1 * diagonal2) / 2
Area of rhombus = (4 * 6) / 2 = 12 cm2

What will be area and perimeter of given trapezium if AB is parallel to CD?

Area of trapezium = (sum of length of parallel side(or bases)) * height / 2.
Area of trapezium = (3 + 4. 5) * 3 / 2 
= 11.25 cm2
Perimeter of trapezium = Sum of all sides
= 3 + 3 + 3.5 + 4.5 = 14 cm


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