Question

A quadrilateral-shaped photo-frame has all sides equal. Which of the following is not a possible shape for the photo-frame?
A) Square
B) Trapezium
C) Rhombus
D) None of these

Answer 1

Hint: Quadrilateral is a closed figure enclosed by four straight lines. It can take various shapes depending on the angles and the length of the sides. Square, rhombus and trapezium are all types of quadrilateral which differs from each other based on their angles and sides. In this question, we have to determine which of the given quadrilaterals does not have all sides equal.

Complete answer:
We have been given that the photo-frame is quadrilateral-shaped with all sides equal. Since we know that a quadrilateral is a four-sided polygon, we have a photo-frame with equal four sides.
Now, we will look at the options one-by-one to determine which of the given options is not possible, i.e. which of the given quadrilaterals does not have all four sides equal. For this we will have to look at the definition of each.

A) Square: A square is a quadrilateral with all four sides and four angles equal. The figure of a square is as shown below. All the four sides are equal with all angles equal to .

B) Trapezium: A trapezium is a quadrilateral which has exactly one pair of parallel sides. The other two sides are non-parallel. As clear from the figure below, the trapezium cannot have all four sides equal to each other. At most it can have three sides equal to each other.

C) Rhombus: A rhombus is a quadrilateral with opposite sides parallel to each other, and all four sides equal. We say it is a parallelogram with all four sides equal. The difference between a rhombus and a square is that the angles in a rhombus are not equal to . The figure of a rhombus is as shown below.


So, now we know that a square and rhombus are quadrilaterals with all four sides equal, whereas a trapezium does not have all four sides equal to each other. Thus, a trapezium is not a possible shape for the given photo-frame.

Hence, option (B) is the correct answer.

Note: A quadrilateral is a polygon with four sides, i.e. it is a closed figure enclosed by four straight lines. Parallelogram, rectangle, square, rhombus and trapezium are all types of quadrilaterals. Square and rhombus have all four sides equal to each other.