rhombus
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What is a rhombus?
A rhombus is a quadrilateral where all four sides have equal length, and each pair of opposite sides are parallel. It is also known as an equilateral parallelogram. The word "rhombus" comes from the Greek word rhombos, meaning "spinning top".
Key characteristics of a rhombus:
* All four sides are equal.
* Opposite sides are parallel.
* Opposite angles are equal.
* Adjacent angles add up to 180°.
* The sum of all interior angles is 360°.
* Diagonals bisect each other at 90°.The area of a rhombus can be found if you know the side and altitude, or the length of the diagonals. Rhombuses are present in everyday life, from traffic signs to jewelry.
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How is a rhombus different from other quadrilaterals?
A rhombus is a four-sided geometric figure, also known as a quadrilateral, with all four sides of equal length and with each pair of opposite sides parallel to each other.
Here's how a rhombus differs from other quadrilaterals:
* All four sides of a rhombus are equal in length.
* Opposite sides of a rhombus are parallel to each other.
* The opposite pairs of angles in a rhombus are equal.
* Any two adjacent angles add up to 180°.
* A rhombus with all interior angles at 90° becomes a square.
* The sum of all interior angles of a rhombus is 360°.
* The diagonals of a rhombus bisect each other at a 90° angle.2 Britannica SourcesCreated from Britannica articles using AI. AI can make mistakes, so verify using Britannica articles. -
What are the properties of the sides and angles of a rhombus?
A rhombus is a quadrilateral where all four sides have equal length, with each pair of opposite sides parallel.
Properties of Rhombus Sides and Angles:
* All four sides are of equal length.
* Opposite sides are parallel to each other.
* The two opposite pairs of angles are equal. For example, if one angle is 60°, the opposing angle is also 60°.
* Any two adjacent angles add up to 180°. For example, if one angle is 55°, the angle next to it will be 125°.
* The sum of all interior angles is 360°.
* If two diagonal lines are drawn across each pair of opposite corners, they will be perpendicular and bisect each other at an angle of 90°. These diagonal lines will also bisect the angles they pass through.1 Britannica SourceCreated from Britannica articles using AI. AI can make mistakes, so verify using Britannica articles. -
How do the diagonals of a rhombus behave?
A rhombus is a quadrilateral where all four sides have equal length, and each pair of opposite sides are parallel.
When drawing two diagonal lines across each pair of opposite corners, they will be perpendicular and bisect each other at a 90° angle. These diagonals will also bisect the angles they pass through.
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How can you calculate the area of a rhombus?
The area of a rhombus can be determined using two methods.
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Method 1: When the side length and altitude (height) are known, the area is calculated by multiplying the side by its altitude: area = altitude × side length. For example: A rhombus with a side length of 5 units and an altitude of 6 units has an area of 30 square units.
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Method 2: When the lengths of the two diagonals are known, the area is calculated by multiplying the lengths of the diagonals, and dividing by two: area = (length of diagonal 1 × length of diagonal 2) / 2. For example: A rhombus with diagonals of length 7 units and 8 units has an area of 28 square units.
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How is a rhombus related to a square and a parallelogram?
A rhombus is a four-sided figure with all sides of equal length and each pair of opposite sides parallel to each other, making it an equilateral parallelogram.
A rhombus relates to both a square and a parallelogram:
* Square A rhombus with all interior angles of 90° becomes a square. A square is both equiangular and equilateral.
* Parallelogram A rhombus is an equilateral parallelogram. A parallelogram is a four-sided figure in which both pairs of opposite sides are parallel and equal.3 Britannica SourcesCreated from Britannica articles using AI. AI can make mistakes, so verify using Britannica articles.
rhombus, a four-sided, or quadrilateral, geometric figure in which all four sides are of the same length and each of the two pairs of opposite sides are parallel to each other. A rhombus is an equilateral parallelogram.
The word rhombus comes from the Greek rhombos, meaning “a spinning top” or “a piece of wood whirled on a string.” Rhombuses (sometimes also called rhombi) can be seen in everyday life, in applications ranging from traffic signboards to jewelry to interior and exterior design.
Properties
A rhombus has several distinct characteristics:
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- All four sides of the rhombus are equal in length.
- Opposite sides of a rhombus are parallel to each other.
- The two opposite pairs of angles within the rhombus are equal to each other. If one angle is 60°, the opposite angle must also be 60°.
- Any two adjacent angles (angles next to each other) within the rhombus add up to 180°. For example, if one angle is 55°, the angle next to it will be 125°.
- A rhombus is also called a diamond. If all four interior angles are 90°, the rhombus becomes a square.
- The sum of all interior angles of a rhombus is always 360°.
- If two diagonal lines are drawn across each pair of opposite corners, they will be perpendicular to and bisect (divide into equal halves) each other at an angle of 90°. These diagonal lines will also bisect the angles they pass through.
Formula for perimeter
The perimeter, or distance around the edges, of a rhombus is calculated by multiplying the length of one side of the rhombus by 4.perimeter of a rhombus = 4 × side lengthIf a rhombus has a side length of 4 units, its perimeter will be 16 units:4 × side length = 4 × 4 = 16
Formulas for area
The area of a rhombus can be calculated using either of two methods. In the first method, the area is calculated by multiplying the side of the rhombus by its altitude (distance between two opposite sides, which can also be called its height):method 1: area of a rhombus = altitude × side lengthA rhombus with a side length of 5 units and an altitude (height) of 6 units will have an area of 30 square units.method 1: area = 5 × 6 = 30 square unitsThis method can be used when both the side length and the altitude are known.
In the second method, instead of the side length, the lengths of the two diagonals (lines joining the pairs of opposite corners) of the rhombus are used. The area is calculated by multiplying the lengths of the two diagonals and dividing by two:method 2: area of a rhombus = length of diagonal 1 × length of diagonal 2/ 2A rhombus with diagonals of length 7 units and 8 units will thus have an area of:method 2: area = 7 × 8/2 = 28 square units
Rhombuses in daily life
Flat gardening and masonry trowels often take the shape of a rhombus. The pointed end makes it easy to dig into the earth or the thick mortar. The broad middle section of the trowel is then used to lift dirt or to lay mortar between bricks or masonry stones.
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A rhombic lattice is a lattice (an interlaced pattern) that has a rhombus as its fundamental design element. Rhombic lattices help portray both two-dimensional and three-dimensional designs. Rhombic lattices are often used in wallpaper, floor and wall tiling, carpeting, and clothing designs. The classic argyle pattern usually seen on socks and sweaters features diamond shapes.
In several countries, including the United States, many traffic departments use diamond-shaped yellow warning signs to indicate potentially dangerous road conditions ahead, such as slippery surfaces, merging lanes, or sharp curves. Other common uses of the rhombus include jewelry designs, as for earrings, pendants, and rings, as well as equilateral kites. A baseball field, or “diamond,” is also a rhombus.
Some modern buildings, such as the Crain Communications Building in Chicago, prominently incorporate this geometric figure in their structure. The logo of the Japanese automaker Mitsubishi features three red rhombuses sharing a common vertex.