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Properties of Rectangle
The properties of a rectangle distinguish it from the other quadrilaterals. A rectangle is an equiangular quadrilateral in which the opposite sides are parallel and equal to each other and all four angles are right angles. The longer side of a rectangle is called its length and the shorter side is the width.
|1.||What are the Properties of a Rectangle?|
|2.||Formulas of a Rectangle|
|3.||Types of Rectangles|
|4.||FAQs on Properties of Rectangle|
What are the Properties of a Rectangle?
The properties of a rectangle help us identify the figure at one glance. A rectangle is a two-dimensional figure with four sides, four vertices, and four angles. The opposite sides of a rectangle are equal in length and are parallel to each other. Since a rectangle is a quadrilateral in which all four angles are equal to each other, the angle formed by its adjacent sides is 90°. Observe the rectangle given below to see that the four sides of a rectangle are not equal, only the opposite sides are equal. Some of the real-life examples of a rectangle that we see in our daily life are kites, paintings, slabs, storage boxes, and so on.
In order to understand the rectangle better, observe the rectangle given above and relate to the following properties of a rectangle.
- A rectangle is a quadrilateral with four equal interior angles.
- The opposite sides of a rectangle are equal and parallel to each other.
- The interior angle of a rectangle at each vertex measures 90°.
- The sum of all the interior angles of a rectangle is 360°.
- The diagonals bisect each other.
- The length of the diagonals is equal.
- The length of the diagonals can be obtained using the Pythagoras theorem. The length of the diagonal with sides a and b is √( a² + b²).
- Since the sides of a rectangle are parallel, it is also called a parallelogram.
- All rectangles are parallelograms but all parallelograms are not rectangles.
Formulas of a Rectangle
- Area of a Rectangle: A = l × w, where 'l' and 'w' are the length and width of the rectangle, respectively.
- Perimeter of a Rectangle: P = 2(l + w), where 'l' is the length and 'w' is the width of the rectangle.
- Diagonal of Rectangle (d) = √(l² + w²), where 'l' is the length and 'w' is the width of the rectangle. The formula for the diagonal of a rectangle is derived from the Pythagoras theorem.
Types of Rectangles
A rectangle has four sides with the opposite sides equal to each other and with the adjacent sides meeting at 90°. These properties are seen in the two types of rectangles - the Square and the Golden Rectangle.
A square is a type of rectangle with four equal sides and four equal angles. It is a two-dimensional shape where the interior angles at each vertex are 90°. Along with these properties, the opposite sides of a square are equal and parallel and the diagonals bisect each other at 90°. It can be said that all squares are rectangles but all rectangles cannot be squares.
The golden rectangle is a rectangle whose sides are in the golden ratio, that is, (a + b)/a = a/b, where 'a' is the width and (a + b) is the length of the rectangle. In other words, a golden rectangle is a rectangle whose 'length to width ratio' is similar to the golden ratio, 1: (1+⎷ 5)/2. For example, if the length is around 1 foot long then the width will be 1.168 feet long or vice-versa where the Golden Ratio = 1: 1.618. Observe the following figure which shows the golden rectangle and its length and width.
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Examples on the Properties of a Rectangle
Example 1: If the length and width of a rectangle are 14 cm and 10 cm, respectively, calculate the area and perimeter of the rectangle.
The area and perimeter of a rectangle can be calculated using the properties of a rectangle. Length of the rectangle = 14 cm; Width of a rectangle = 10 cm
Area of a rectangle: Length × Width
14 × 10 = 140 cm2
Perimeter of a rectangle = 2 (length + width)
2 (14 + 10) = 24 × 2 = 48 cm
Example 2: George has a rectangular photo frame that is 11 inches long and 8 inches wide. Can you help George find its area?
According to the properties of a rectangle, Area of a Rectangle = (Length × Width). Thus, the area of the rectangular frame = 11 × 8 = 88 square inches
Therefore, the area of the photo frame = 88 inches2
Example 3: The perimeter of a rectangular pool is 86 meters. If the length of the pool is 40 meters, then find its width using the properties of rectangle.
The formula to calculate the perimeter is P = 2 (length + width);
Given that, the perimeter is 86 meters and the length is 40 meters. Substituting these values into the formula.
86 = 2(40 + w)
86 = 80 + 2w
6 = 2w
w = 3
Therefore, the width of the rectangular pool is 3 meters.
FAQs on Properties of Rectangle
What are the Properties of a Rectangle?
The basic properties of a rectangle are that its opposite sides are parallel and equal and its interior angles are equal to 90°. Its diagonals are also equal and they bisect each other.
What are the Properties of the Diagonals of a Rectangle?
The properties of the diagonal of a rectangle are as follows:
- The two diagonals of a rectangle are equal.
- The diagonals bisect each other, but not at right angles.
- The length of the diagonals can be obtained using the Pythagoras theorem.
- Since the diagonals divide the rectangle into two right-angled triangles, they are considered to be the hypotenuse of these triangles.
Is a Square a Rectangle?
Yes, a square is considered as a rectangle as it contains the properties of a rectangle, like, all the four interior angles are 90°, the opposites sides of a square are parallel and equal to each other, and two diagonals of the square are equal and bisect each other.
What is the Difference Between a Square and a Rectangle
Squares have some additional properties which do not apply to rectangles. A square has four equal sides, whereas, in a rectangle, only the opposite sides are equal. The diagonals of a square bisect at 90°, but the diagonals of a rectangle do not bisect at 90°.
What are the Various Types of Quadrilaterals other than Rectangles?
Why is a Rectangle not a Square?
A rectangle does not have all four sides of equal measure. This is the reason that a rectangle is not a square.
What is a Rectangle?
A rectangle is a two-dimensional shape (2D Shape) with four sides, four angles, and four vertices. The opposite sides of a rectangle are equal and parallel to each other. The interior angles of a rectangle are equal and measure 90°.