Rhombus Questions and Answers

1. What is a Rhombus?

A Rhombus is a quadrilateral with all equal sides. Since opposite sides of a parallelogram are equal so, rhombus is a special type of parallelogram whose all sides are equal.

1.1 Properties of a Rhombus

• All sides of a rhombus are equal.

        AB =  BC = CD = AD.

• Opposite sides are parallel. 

         AB is parallel to CD and BC is parallel to AD.

• Opposite angles are equal. 

        a = c, b = d.

• Adjacent angles add up to 180o.

        a + b = 180°, b + c = 180°, c + d = 180°, d + a = 180°

•  All the interior angles of a rhombus add up to 360°.

        a + b + c + d = 360°

• The diagonals of a rhombus intersect each other at a right angle.
• It has two lines of symmetry and two orders of rotational symmetry.

1.2 Perimeter of a Rhombus

The perimeter of a rhombus is the total length of its boundaries. As all the four sides of a rhombus are equal, its perimeter is calculated by multiplying the length of its side by 4.

Perimeter of the Rhombus = (4 × side)

1.3 Area of a Rhombus

              The area of a rhombus is the amount of space inside the rhombus. It is measured 

               In square units.

               There are two ways to work out the area of rhombus.

              a) Area of rhombus when base and perpendicular height is given.

b = Base and h = Perpendicular height

                   Area of rhombus = b × h sq. units

              b) Area of rhombus when diagonals are given.

                        d1 and d2 are the length of diagonals.

                        Area = d1 × d2 ÷ 2 sq. units