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Question

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$ \begin{align}

& \text{a) Square} \\

& \text{b) Rhombus} \\

& \text{c) Rectangle} \\

& \text{d) Trapezium} \\

\end{align} $

Answer
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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.