GRE Geometry | Quadrilaterals (original) (raw)

Last Updated : 11 Jul, 2025

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:

• **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)
• **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
• **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
• **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.
• **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 congruent to each other.
  • Opposite angles are congruent to each other.
  • Sum of adjacent angles is 180°
  • Diagonals of parallelogram bisect each other and divide the parallelogram into two congruent 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 area 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