Rectangle

A rectangle has four sides.

It has four square corners. These corners are called right angles. All four corners are the same size.

The sides can be long or short. A square is a special rectangle. In a square, all four sides are equal. You see rectangles in brick walls. You see them in many patterns. They are everywhere around us!

A rectangle is a shape with four sides.

It has four right angles. A right angle is a square corner. All four corners are the same size. Each corner is 90 degrees. Because the corners are equal, we call it an equiangular shape.

A rectangle can be a special type of parallelogram. A parallelogram is a shape where opposite sides are parallel. In a rectangle, the opposite sides are also equal in length. If all four sides are the same length, it is a square. Some people call a rectangle that is not a square an oblong.

You can find rectangles in many patterns. For example, bricks in a wall often form rectangles. They can be laid in a stacked bond or a running bond. You might also see a basket weave pattern.

There are also crossed rectangles. These look like a bow tie or a butterfly.

They use two sides and two diagonals. In other math worlds, like on a sphere, rectangles can have different angles. But in our flat world, they always have four right angles.

A rectangle is a special kind of shape with four straight sides.

We call these shapes quadrilaterals. To be a rectangle, the shape must have four right angles. A right angle is a perfect square corner. Because all four corners are the same, we say the shape is equiangular.

In our flat world, every corner in a rectangle is exactly 90 degrees. This makes the shape very steady and easy to recognize.

There are many ways to describe how a rectangle works. You can think of it as a parallelogram that has at least one right angle. A parallelogram is a shape where opposite sides run in the same direction and never meet. In a rectangle, the two diagonals, which are lines connecting opposite corners, are exactly the same length.

If you make all four sides of a rectangle the same length, it becomes a square. Some people use the word "oblong" to describe a rectangle that is not a square. You can find the area of a rectangle by multiplying its length by its width.

The word rectangle has a history rooted in old languages. It comes from the Latin words "rectus" and "angulus." The word "rectus" means right or proper. The word "angulus" means angle.

When you put them together, you get a name that describes its right angles. There are also unusual versions like the crossed rectangle. This shape looks like a bow tie or a butterfly. It uses two opposite sides and two diagonals to create its shape.

Rectangles show up in many interesting places and math problems. You can use them to cover a flat surface, which is called tiling.

Bricks in a wall often use rectangle patterns. You might see a stacked bond or a running bond pattern. Other patterns include the basket weave or the herringbone pattern.

Mathematicians even study "perfect" rectangles. A perfect rectangle is one tiled by smaller squares that are all different sizes. The smallest number of squares needed to make a perfect rectangle is nine.

You can see the logic of rectangles in the world around you. Many things we use, like books or screens, are shaped like rectangles. They are easy to stack and line up in rows.

Even in different math worlds, like on a curved sphere, rectangles exist. On a sphere, the sides are arcs and the angles are larger than 90 degrees. Whether they are flat or curved, these shapes help us organize space and measure the world.

A rectangle is a specific type of quadrilateral, which is a polygon with four sides. In Euclidean plane geometry, it is defined as a rectilinear convex polygon with four right angles. Because all four of its angles are equal, a rectangle is also known as an equiangular quadrilateral. Each of these angles measures exactly 90 degrees.

This shape is a special case of a parallelogram. A parallelogram is a quadrilateral where opposite sides are parallel and equal in length. If a parallelogram contains at least one right angle, it must be a rectangle.

There are several ways to identify a rectangle through its geometric properties. A convex quadrilateral is a rectangle if its diagonals are equal in length and bisect each other. This means the diagonals cut each other exactly in half. Another way to define it is as a parallelogram where the diagonals are of equal length. You can also identify a rectangle if it is a parallelogram where each pair of adjacent sides is perpendicular. This perpendicular relationship is what creates the characteristic right angles.

Furthermore, the area of a rectangle is calculated as the product of its length and width. If the length and width are equal, the rectangle becomes a square.

Rectangles belong to a specific hierarchy of shapes. A rectangle is a special type of parallelogram. A parallelogram is itself a special type of trapezium, which is a convex quadrilateral with at least one pair of parallel sides. In North America, the term trapezoid is often used instead of trapezium. Within the rectangle family, a square is a special case where all four sides are of equal length. When a rectangle is not a square, it is sometimes referred to as an oblong.

The history of the word rectangle is found in the Latin language. It is derived from the combination of "rectus," meaning right or proper, and "angulus," meaning angle. This name literally describes the right angles that define the shape. Beyond standard flat geometry, different mathematical systems contain their own versions of rectangles. In spherical geometry, a spherical rectangle has edges that are great circle arcs with angles greater than 90 degrees. In hyperbolic geometry, the angles are less than 90 degrees.

Rectangles possess unique symmetry and duality. A rectangle is cyclic, meaning all four of its corners lie on a single circle. It also has two lines of reflectional symmetry that pass through the midpoints of opposite sides. It possesses rotational symmetry of order 2, which means it looks the same after a 180-degree turn. Interestingly, the rectangle has a duality with the rhombus. While a rectangle has equal angles, a rhombus has equal sides. If you join the midpoints of the sides of a rectangle, the resulting shape is a rhombus.

Mathematics also explores more complex versions, such as the crossed rectangle. A crossed rectangle is a self-intersecting quadrilateral. It is formed by two opposite sides of a rectangle and its two diagonals. This shape often resembles a bow tie or an angular eight. While it shares some properties with standard rectangles, such as equal diagonals and opposite sides, its angles are not right angles.

There are also saddle rectangles, which involve four nonplanar vertices that create a saddle-shaped surface in three dimensions.

Rectangles are essential in the study of tiling, or tessellation. This involves covering a plane with shapes without gaps or overlaps. Common tiling patterns using rectangles include the stacked bond, running bond, basket weave, and herringbone patterns.

Mathematicians also study "perfect" rectangles. A perfect rectangle is one that is tiled by smaller squares where no two squares are the same size. The lowest number of squares required to create a perfect rectangle is nine.