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# 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

## 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.       Talk to our expert
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