Difference between Square and Rhombus

Square

A plane figure or a quadrilateral with equal sides and equal angles is called a square. All the angles present in a square are right-angled.

Properties of a square

All sides are equal
All angles are equal
All angles are right-angled
All the sides are congruent to each other
Opposite sides are parallel to each other
Diagonals bisect each other equally
Diagonals bisect at 90°
Equal diagonals of a square make two similar isosceles triangles

Rhombus

A diamond-shaped quadrilateral is called a rhombus. It is also called a parallelogram with equal sides. In a rhombus, the opposite sides and angles are equal in length and are parallel to each other. The diagonals bisect each other at 90°, just like the square.

Properties of a rhombus

All sides are equal
Opposite sides are parallel to each other
Diagonals bisect the angles
Diagonals bisect at 90°
No inscribing and circumscribing circles can be made around the rhombus
Adjacent angles of a rhombus add up to 180°

Similarities between a square and a rhombus

square	Rhombus
Is a quadrilateral	Is a quadrilateral
Diagonals bisect each other at right angles	Diagonals bisect each other at right angles
Sum of all interior angles is 360°	Sum of all interior angles is 360°
Opposite sides are equal and parallel	Opposite sides are equal and parallel
All sides are equal in length	All sides are equal in length
Is considered a parallelogram	Is considered a parallelogram

Differences between a Square and a Rhombus

square	Rhombus
All angles are equal to 90°	Only opposite angles are equal to each other
Diagonals are equal in length	Diagonals aren’t equal in length
Can be inscribed in a circle	Cannot be inscribed in a circle
Has four lines of symmetry	Has two lines of symmetry
Sides are perpendicular to each other	Sides aren’t perpendicular to each other

Square

The formula used to calculate the area = s x s, where 's' is the length of the side of a square.

The formula used to calculate the Perimeter = 4 x s, where 's' is the length of the side of a square.

Rhombus

The formula used to calculate the area = (s₁ x s₂) / 2, where s1 and s2 are the lengths of the diagonals.

The formula used to calculate the perimeter = 4 x s

1. Assume quadrilateral MNOP is a rhombus. If diagonal MO=29 and diagonal NP=14, what is the area of rhombus MNOP?
Solution: Solving for the area of rhombus MNOP requires knowledge of the equation for finding the area of a rhombus. The equation is A=pq / 2, where p and q are the two diagonals of the rhombus. Since both of these values are given to us in the original problem, we merely need to substitute these values into the equation to obtain:

A = (29)(14) / 2
= 406 / 2
=203

The area of rhombus MNOP is therefore 203 square units.

Find the area of a square of side 35 m.
Solution:
Area of a square = length × length
= 35 × 35 sq. m.
= 1225 sq. m.

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