Question

# What is the name of a parallelogram with all sides equal? \begin{align} & \text{a) Square} \\ & \text{b) Rhombus} \\ & \text{c) Rectangle} \\ & \text{d) Trapezium} \\ \end{align}

Hint: Now any figure with 4 sides is called Quadrilateral. In a parallelogram opposite sides are equal and parallel. Also the opposite angles of parallelogram are equal.

Any figure which has 4 sides and 4 vertices is called a Quadrilateral.
Now each different Quadrilateral has its own definition.
A Parallelogram is a Quadrilateral with its parallel side equal and opposite as well as its opposite angles are equal.

A Square is Quadrilateral with opposite sides parallel, all sides equal and all the angles are equal.

A Rhombus is a Quadrilateral with opposite sides parallel and all sides equal

A Rectangle is a Quadrilateral with all opposite sides equal and parallel and all the angles are equal.

A Trapezium is a quadrilateral with one pair of opposite sides parallel

Now, Consider a Parallelogram with all sides equal.
If all its sides are equal we get a parallelogram with opposite sides parallel and opposite angles equal as well as all its sides are also equal.
Now we know that a Quadrilateral with all its side equal and opposite angles also equal is a Rhombus.
Hence, the name of the parallelogram with all sides equal will be Rhombus.
Now since the angles are not all equal the Quadrilateral cannot be a Square or Rectangle.
Also since both opposite sides are parallel the Quadrilateral is not a Trapezium.
So, the correct answer is “Option B”.

Note: Rhombus can sometimes be confused with square since both the quadrilaterals have a common property that all its sides are equal. However the thing that distinguishes a Rhombus from a square is the property that all the angles of the square are also equal and in fact each angle is equal to 90° while in Rhombus just the opposite angles are equal. Hence, we can say that every square is a Rhombus but every Rhombus need not be a square.