Rectangle
A rectangle is a quadrilateral with four right angles. The following are two examples.
![](/img/a/geometry/shapes/rectangle/rectangle.png)
Rectangles are one of the most common shapes you will see in daily life. Many objects around us are rectangular in shape, such as a book, a phone, a door, a card, and many more.
![](/img/a/geometry/shapes/rectangle/rectangle-examples.png)
Sides of a rectangle
The opposite sides of a rectangle are congruent and parallel to each other. The longer sides of a rectangle are typically referred to as its length while the shorter sides are referred to as its width.
![](/img/a/geometry/shapes/rectangle/rectangle-sides.png)
Angles of a rectangle
A rectangle contains four interior right angles. Angles A, B, C and D equal 90° in the rectangle shown below.
![](/img/a/geometry/shapes/rectangle/rectangle-angles.png)
Diagonals of a rectangle
There are two diagonals in a rectangle. The two diagonals (right triangles.
and in the rectangle below) are congruent and bisect each other. Each diagonal divides the rectangle into two congruent![](/img/a/geometry/shapes/rectangle/rectangle-diagonals.png)
Diagonal
divides rectangle ABCD into triangles ABD and CDB. ≅ and ≅ since opposite sides of a rectangle are congruent. ∠A≅∠C since the interior angles of a rectangle are right angles. Therefore, △ABD≅△CDB by the Side-Angle-Side postulate.Square
A square has four congruent sides and four right angles, so it is also a rectangle. A rectangle is a square when all of its sides are congruent.
![](/img/a/geometry/shapes/rectangle/square.png)
Symmetry in a rectangle
A rectangle has 2 lines of symmetry and a rotational symmetry of order 2, which means that it can be rotated in such a way that it will look the same as the original shape 2 times in 360°.
Lines of symmetry | Rotational symmetry |
---|---|
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2 lines of symmetry | two 180° angles of rotation |
Area of a rectangle
The area of a rectangle is the product of its length and width.
A = l·w
Where l is the length and w is the width of the rectangle. Some textbooks might write the dimensions of a rectangle as base and height instead of length and width.
![](/img/a/geometry/shapes/rectangle/rectangle-area.png)
Did you know?
A golden rectangle is a rectangle in which the ratio of its length to its width is the golden ratio. For the rectangle below with a length of (a + b) and width of a, =φ, where φ is the golden ratio and is equal to approximately 1.618. The rectangle shown below in purple also satisfies the golden ratio:
=φ.
![](/img/a/geometry/shapes/rectangle/golden-rectangle.png)