What is the Difference Between a Rhombus and a Square | Properties, Formulas, and More

Rhombus and Square

A rhombus and a square are both quadrilaterals, meaning they have four sides

A rhombus and a square are both quadrilaterals, meaning they have four sides. While they share some similarities, they also have distinctive properties that set them apart.

1. Rhombus:
– Definition: A rhombus is a quadrilateral with all sides of equal length. In other words, all four sides of a rhombus are congruent.
– Properties: Some key properties of a rhombus are:
– Opposite sides are parallel: The opposite sides of a rhombus are always parallel to each other.
– Opposite angles are congruent: The opposite angles of a rhombus are equal.
– Diagonals bisect each other: The diagonals of a rhombus intersect at a 90-degree angle and bisect each other, meaning they divide each other into two equal parts.
– Diagonals are not equal in length: Unlike a square, the diagonals of a rhombus are not of equal length.
– Formulas:
– Area: To calculate the area of a rhombus, you can use the formula A = (d1 * d2) / 2, where d1 and d2 are the lengths of the diagonals.
– Perimeter: The perimeter of a rhombus is simply the sum of all four side lengths.

2. Square:
– Definition: A square is a special type of rhombus with all sides of equal length and all angles equal to 90 degrees.
– Properties: Some key properties of a square are:
– All sides are congruent: In a square, all four sides have the same length, making them congruent.
– All angles are right angles: Each angle of a square measures exactly 90 degrees.
– Diagonals are equal in length: Unlike a rhombus, the diagonals of a square are of equal length and bisect each other at 90 degrees.
– Diagonals divide the square into congruent right triangles: The diagonals split the square into four congruent right triangles.
– Formulas:
– Area: To calculate the area of a square, you can use the formula A = side^2, where side represents the length of any side of the square.
– Perimeter: The perimeter of a square is simply the sum of all four side lengths, each of which is equal.

In summary, a rhombus is a quadrilateral with all sides equal in length, while a square is a special type of rhombus with the added property of having all angles equal to 90 degrees. Both shapes have distinct properties and formulas for calculating their areas and perimeters.

More Answers:
Understanding the Basics and Properties of Triangles in Geometry
Exploring the Properties and Applications of Regular Polygons in Mathematics and Beyond
Differences between a Rectangle and a Square | Properties, Angles, Symmetry, and Special Case

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