A rectangle is a type of quadrilateral. In fact, it is also called equiangular quadrilateral as all the angles are equal. There are many rectangular objects around you. Each rectangular shape is characterized by two dimensions, its length, and width. The longer side of the rectangle we call is the length and the shorter side is called width. In this chapter, we will learn about rectangle shape and its properties.
|1.||What is a Rectangle?|
|2.||Diagonal of a Rectangle|
|3.||Area of a Rectangle|
|4.||Perimeter of a Rectangle|
|5.||Properties of a Rectangle|
|6.||FAQs on Rectangle|
What is a Rectangle?
A rectangle is a closed two-dimensional figure with four sides and four corners. The length of the opposite sides is equal and parallel to each other. The adjacent sides of a rectangle are meet at the right angle that is, the angle formed by the adjacent sides of a rectangle is 90°. The basic feature of a rectangle is given below.
Diagonal of a Rectangle
The diagonal of a rectangle is a line segment that joins any two of its non-adjacent vertices. In the following rectangle, AC and BD are the diagonals. You can see that the lengths of both AC and BD are the same. A diagonal cuts a rectangle into 2 right triangles, in which the sides equal to the sides of the rectangle and with a hypotenuse. That hypotenuse is the diagonal.
Diagonal of Rectangle Formula
The formula for the diagonal of a rectangle is derived using the Pythagoras theorem. The length of the diagonal of the Rectangle is found using the formula shown below. Let us consider a rectangle of length "l" and width "w". Let the length of each diagonal be "d". Applying Pythagoras theorem to the triangle ABD, d2 = l2 + w2. Taking square root on both sides, √(d2) = √( l2 + w2). Thus, the diagonal of a rectangle formula is: √(l² + w²) and thus the diagonals of a rectangle can be calculated when the length and width of the rectangle are known.
Diagonal of Rectangle (d) = √(l² + w²)
Area of a Rectangle
The area of a rectangle is the number of unit squares that can fit into a rectangle. Some examples of rectangular shapes are the flat surfaces of laptop monitors, blackboards, painting canvas, etc. You can use the formula of the area of a rectangle to find the space occupied by these objects. For example, let us consider a rectangle of length 4 inches and width 3 inches. Let us draw unit squares inside the rectangle. Each unit square is a square of length 1 inch. Now, count the number of unit squares in the above figure. How many squares can you observe? There are 12 squares in total. We have already learned that area is measured in square units. Since the unit of this rectangle is "inches," the area is measured and written in square inches. Thus, the Area of the above rectangle = 12 square inches. Thus, the area of a rectangle can be calculated when its sides(length and breadth) are known.
Area of Rectangle Formula
The formula for the area, 'A' of a rectangle whose length and width are 'l' and 'w' respectively is the product "l × w".
Area of a Rectangle = (Length × Width) square units
Perimeter of a Rectangle
The perimeter of a rectangle is the length of the outer boundary of a rectangle. It can be taken as the sum of the total measure of the length and breadth of the rectangle. The perimeter of a rectangle helps us in calculating distances and lengths in our day-to-day lives. For example, if you need to decorate the border of your rectangular notebook, you can easily calculate how much ribbon you would need by finding the perimeter or if you need to put a fence around your garden, the perimeter of the garden will give you the exact length of wire you would need. The formula used to calculate the perimeter of a rectangle is:
Perimeter of Rectangle Formula
The formula for the perimeter, 'P' of a rectangle whose length and width are 'l' and 'w' respectively is 2(l + w).
Perimeter of a Rectangle Formula = 2 (Length + Width) units
Properties of a Rectangle
A rectangle is a closed figure of four sides having two equal pairs of opposite sides and the angle formed by adjacent sides is 90 degrees. A rectangle can have a wide range of properties. Some of the important properties of a rectangle are given below.
- A rectangle is a quadrilateral.
- The opposite sides of a rectangle are equal and parallel to each other.
- The interior angle of a rectangle at each vertex is 90°.
- The sum of all interior angles is 360°.
- The diagonals bisect each other.
- The length of the diagonals is equal.
- The length of the diagonals can be obtained using the Pythagorean 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.
- If two diagonals bisect each other at 90°, it forms a square.
Types of Rectangles
A two-dimensional geometry having four sides whose opposite sides are equal and adjacent sides meets at 90° is called a rectangle. A rectangle is having two equal diagonals. The length of the diagonals is calculated by using their length and width. There are two types of rectangles:
- Golden Rectangle
A square is a closed two-dimensional shape with four equal sides and four equal angles. It is a type of rectangle in which all four sides are equal. The interior angle at each vertex is 90º which satisfies the definition of the rectangle.
A golden rectangle is a rectangle whose length to the width ratio is similar to the golden ratio, 1: (1+⎷ 5)/2. It is approximately derived as Golden Ratio = 1: 1.618. For instance, if a length is about 1 foot long then the width will be 1.168 feet long or vice-versa.
Example 1: George orders for a rectangular photo frame that is 6 inches long and 3 inches wide. Can you help George find its area?
We know the formula to calculate the area of a rectangle. Area of a Rectangle = (Length × Width) square units. Thus, the area of rectangular frame = 6 × 3 = 18 square inches
Therefore, the area of the photo frame = 18 square inches
Example 2: Elsa wants to build a rectangular fence for her garden. The perimeter of the fence is 30 feet. The width of the fence is 10 feet. Can you help Elsa find the length of the fence?
We know the formula to calculate the perimeter of a rectangle.Perimeter of a Rectangle = 2 (Length + Width) units. We have perimeter = 30 feet and width = 10 feet, 30 = 2 (Length + 10). Since, length + 10 = 15, this implies, 15 - 10 = 5
Therefore, the length of the fence = 5 feet
FAQs on Rectangle
What is An Irregular Rectangle Called?
A rectangle whose length is not equal and angles differ from each other is called an irregular rectangle.
Why is a Rectangle Not a Regular Polygon?
A regular polygon is a polygon whose length is equal on all sides with equilateral angles. But in a rectangle, the length is equal and parallel only on the opposite sides. Hence, the rectangle is not a regular polygon.
What is the Formula for the Area of a Rectangle?
The area of a rectangle is the space occupied by the rectangle. The area of a rectangle is the product of its length and width. The formula for calculating the area of a rectangle is: Area = L × B; where (L) is the length and (B) is the width of the rectangle.
What are the Properties of a Rectangle?
The basic properties of a rectangle are:
- The opposite sides are parallel and equal.
- All the angles are equal to 90°.
- The diagonals are equal and they bisect each other.
Is the Area of the Rectangle the Same as the Area of the Square?
No, the area of the square is not necessarily the same as the area of the rectangle because every square is a rectangle with length and breadth equal but all rectangles are not square. The formula to calculate the area of a rectangle is Length × Breadth and that of the square is (side)2.
How to Find the Perimeter of a Rectangle?
The perimeter of a rectangle is twice the sum of its length and breadth. Perimeter = 2 (Length + Width) units. Perimeter is the sum of the lengths of the boundaries of the rectangle. Hence the perimeter of a rectangle has the same units as the length of the rectangle.