 Area of Rectangle: A rectangle is a 2-D plane figure that has 4 sides and 4 internal angles. In a rectangle, the opposite sides and angles are the same in value. A rectangle is defined as a quadrilateral figure having four sides and the opposite sides are similar in length and parallel to one another. In our day-to-day life, we see several rectangular-designed stuff like tables, books, boxes, mobile phones, walls, television, beds, almirah, etc. In this article, we provide you with the properties of a rectangle, the area of a rectangle, its formulas, and some relevant question answers for a better understanding of the concepts of the rectangle.

## Area of Rectangle

In the study of geometry, the area of a rectangle is defined as the region enveloped by the rectangle in a 2-dimensional plane. All four internal angles of a rectangle are right angles (90°). The surface area extended by a rectangle depends on its four sides. The formula for the area of a rectangle is equivalent to the multiplication of the length and breadth of the rectangle. The rectangular region covered by the perimeter of the rectangle is the area of a rectangle.

## Area of Rectangle Formula

The rectangle area is the region covered inside the outer boundary of the rectangle made by its four sides. The area of a rectangle can be enumerated by the product of its breadth and its length

Let the length of a rectangle is ‘L’ and its breadth or width be ‘B’ and the Area of a Rectangle be indicated by ‘A’. Then the formula to find out the rectangle area will be the product of length and breadth. The area of any figure like a rectangle or else is always represented in square units.

Area of Rectangle= Length × Width

A = L × B (in square units)

### Area of Rectangle Formula’s Proof

The diagonals of a rectangular shape bisect the shape into 2 similar right-angled triangles. Hence, the rectangle area is equivalent to the addition of the area of two right-angled triangles.

Let ABCD is a rectangular shape

Now considering diagonal AC bisects the rectangle into two right-angled triangles like ∆ABC and ∆ADC.

As we know that ∆ABC and ∆ADC are identical right-angled triangles.

Area of ∆ABC = ½ x Base of ∆ABC x Height of ∆ABC =  ½ x AB x BC =  ½ x B x L ……….1

Area of ∆ADC = ½ x Base of ∆ADC x Height of ∆ADC = ½ x CD x AD =  ½ x B x L ……….2

Since Area of Rectangle ABCD = Area of ∆ABC + Area of ∆ADC

From the 1st and 2nd expressions, we have

Area of ABCD Rectangle = 2(½ x B x L)

Area of ABCD Rectangle = L x B

Hence proved that the Area of a Rectangle is = Length x Breadth (Width)

## Area of Rectangle Using Diagonals

The rectangle area can be calculated with the help of its diagonals as given below.

By applying the Pythagoras Theorem, we get

(Diagonal)² = (Length)² + (Width)²

(Length)² = (Diagonal)² – (Width)²

Length = √ (Diagonal)² – (Width)² ……….1

(Width)² = (Diagonal)² – (Length)²

Width = √(Diagonal)² – (length)² …………2

As we know that the rectangle area is the multiplication of length and width

Area of Rectangle = Length × Width

By putting the 2nd equation of width, we get

Area of Rectangle = Length × √(Diagonal)² – (Length)²

By putting the 1st equation of length, we get

Area of Rectangle = √ (Diagonal)² – (Width)² × width

## Rectangle Properties

There are many properties of a rectangle 2-D plane figure which is used in geometry. The key properties of a rectangle are mentioned below.

1. A rectangle is a kind of quadrilateral-shaped figure.
2. The opposite sides of a rectangle are similar in length and parallel to one another.
3. The four interior angles of a rectangle have values of 90° at each vertex.
4. The addition of all four interior angles of a rectangle results in 360° (90°+90°+90°+90°).
5. The rectangle diagonals bisect one another.
6. The two diagonals of a rectangle are the same in terms of their length.
7. The diagonal length can be calculated by using the Pythagoras Theorem. If the diagonal length with sides a and b then the length of the diagonal is = √( a² + b²).
8. When all four sides of a rectangle are parallel in nature then it is called a parallelogram.
9. It is to be noted here that all rectangles are considered parallelograms surely but all parallelograms can not be called rectangles.

## Area of Rectangle Solved Questions

Question 1: If the length of a rectangle is 12 cm and the breadth of that rectangle is 7 cm. Calculate the area of that rectangle.

Solution: Given that Length L = 12 cm and Breadth B = 7 cm

As we know the Area of Rectangle A = L × B

By substituting the values of L and B in the above formula, we get

A = 12 × 7

A = 84 cm²

Question 2: The width of a table is 15 m and the area of that table is 135 m². Find out the length of that table.

Solution: Given that Width of the table = 15 m

and the Area of the table = 135 m²

As we know that table is generally rectangular-shaped so the area of the rectangle will be applied here.

Area of Rectangle = Length × Breadth

A = L × B

135 = L x 15

Length of the table L = 135 / 15 = 9 m

Question 3: Calculate the surface area of a rectangular smartboard in square meters whose length is 200 cm and width is 120 cm.

Solution: First convert the unit from cm to m, 1 meter = 100 cm

Length of the smartboard = 200 cm = 2 m

Breadth of the smartboard = 120 cm = 1.2 m

Area of the smartboard = Area of a Rectangle = Length x Width = 2 m x 1.2 m = 2.4 metres²

Question 4: The length and width of a rectangular wall are given with values of 30 m and 15 m respectively. Calculate the painting cost of that wall if the painting rate is Rs 2 per sq. m.

Solution: Length of the rectangular wall = 30 m

The width of the rectangular wall = 15 m

Area of that rectangular wall = Length of wall x Width of wall = 30 m x 15 m = 450 m²

The painting cost for the coverage of 1 m² is Rs 3

Hence the painting cost for the coverage of 2400 m² will be = 3 x 450 = Rs 1350

Question 5: The length of a book is 5 cm. Its area is 20 sq. cm. What will be its width?

Solution: Given that the Area of the book = 20 sq. cm.

Length of the book = 5 cm

As we know the Area of a rectangle is = Length x Width

Hence, the width can be calculated by = Area / Length

So width of the book = 20/5 = 4 cm

Area of Rectangle: FAQs

Ans. A rectangle is a 2-D plane figure that has 4 sides and 4 internal angles.

Ans. The rectangle area is the region covered inside the outer boundary of the rectangle made by its four sides.

Ans. The formula for the area of the rectangle is described as the product of its width and length. It is represented by Area of Rectangle = Length × Breadth