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.

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