[Maths Class Notes] on Area of Rectangle Pdf for Exam

A quadrilateral whose parallel sides are equal to each other and all the vertices are perpendicular to each other is called a rectangle. The number of unit squares that can fit into any shape, is the area of that shape. Therefore, the area of a rectangle is equal to the number of unit squares that can fit into the boundaries of a rectangle. The area of a shape is measured in terms of the number of square units such as square feet, square inch, square centimeters and so on. Some examples of rectangle shapes are- mobile screens, blackboard, doors, etc.

Any closed shape made up of at least three-line segments is known as a polygon. There are many different types of polygons, some of them being triangles, quadrilaterals, pentagons hexagons etc. The polygons are classified by the number of edges they have. Edges are also called sides, and they are nothing but the line segments which make up the polygons. The points where the line segments intersect are called vertices. A polygon has an equal number of edges and vertices.

Polygons are classified based on the number of edges or vertices they have. A polygon with four sides is called a quadrilateral or tetragon. Quadrilaterals can be further classified into concave quadrilaterals, convex quadrilaterals, and right-angled quadrilaterals based on the angles they contain. If all four sides of the quadrilateral are 90°, they are right-angled quadrilaterals. They are also called equiangular quadrilaterals since all their angles are equal. The two types of equiangular quadrilaterals are squares and rectangles. In a square all the four sides of the quadrilateral are equal. In a rectangle, only the opposite sides of the quadrilateral are equal.

()

Since the opposite sides of the square are equal, the square can also be considered as a rectangle. The rectangle is also a parallelogram, which means the opposite sides of the rectangle are perfectly parallel to each other. We can also say that a rectangle with all four sides equal to each other is a square.

Area of a Rectangle

The area of any polygon is the amount of space it occupies or encloses. It is the number of square units inside the polygon. The area is a two-dimensional property, which means it contains both length and width. The area is usually measured in units like square meters, square feet, or square inches. Area of larger shapes, like fields or cities is measured in square kilometers, hectares, or acres.

()

To find the area of a rectangle, we simply need to multiply its length by its width.

The area is simply the width of a rectangle times height.

The formula to calculate the area of a rectangle is given as

Area = w × h 

For example, if a rectangle is 8 m wide and 3 m high,

The area of the rectangle is Area = w × h 

Area = 8 × 3

Area = 24 m²

In a square, since all the four sides are equal, Area = w × h becomes 

Area = h × h, Area = h².

Hence for a square, the area is the square of its sides.

Formula of Area of Rectangle

The mathematical formula used to calculate the area of a rectangle within its boundary is-

Area of a rectangle= (Length x Breadth) square units

A= l x b

Area of a rectangle is given by the products of its length and width(breadth). 

Steps to Calculate the Area of Rectangle

To find the area of a rectangle follow the steps given below-

1. From the given data, note the dimensions of the length and width. 

2. Multiply the length with the width of the rectangle.

3. The result will be given in square units.
   

Example- The length and width of a rectangle is 8 units and 4 units respectively. Find the area of the rectangle.

Solution– Given, 

length =8 unit

width=4 units

Area of rectangle= l x b

= 8 x 4

=32 square units

Derivation of Area of Rectangle

The lengths and breaths of a rectangle ABCD are AB, CD BC, and AD respectively.

A diagonal AC is drawn in a rectangle ABCD.

AC will divide the rectangle ABCD into two triangles ADC and ABC which are congruent.

The area of rectangle ABCD will be the sum of the triangle ABC and ADC

Area of rectangle ABCD= Area of triangle ABC + Area of triangle ADC

Since the triangles are congruent.

Area of rectangle ABCD= 2 x Area of triangle ABC

                                    =2 x (½ x Base x Height)

           =AB x BC

Area of rectangle ABCD = Length x Breadth

Problems Relating to the Area of a Rectangle

1) Find the area of a rectangle whose height is 20 cm and width is 4 cm.

Solution: Given, Height = 20 cm and Width = 4 cm

Area of a rectangle = w × h

Area of a rectangle = 20 × 4

Therefore, the area of the rectangle = 80 cm².

2) A rectangular board has a width of 120 mm and a height of 89 mm. Find the area of this board.

Solution: Given, Height = 89 mm = 8.9 cm, and Width = 120 mm = 12 cm

Area of a rectangle = w × h

Area of a rectangle = 12 × 8.9

Therefore, the area of the rectangle = 106.8 cm².

3) The height of a rectangular screen is found to be 20 cm. Its area is found to be 240 cm². Find the width of the given screen.

Solution: Given, Height = 20 cm and Area = 240 cm².

Area of a rectangle = w × h

Therefore, Width = Area / length

Width = 240/20

Width = 120 cm

4) The height and width of a rectangular wall are 80 m and 60 m respectively. If a painter charges ₹ 3 per m² for painting the wall, how much would it cost to have the whole wall painted?

Solution: Given, Height = 80 m and Width = 60 m

Area of a rectangle = w × h

Area of a rectangle = 80 × 60

Area of a rectangle = 4800 m²

At the cost of ₹ 3 per m², the cost for painting 4800 m² is 4800 × 3 = ₹ 14,400

5) A floor whose length and width are 60 m and 40 m respectively needs to be covered by rectangular tiles. The dimension of the selected floor tiles is 1 m × 2 m. Find the total number of tiles needed to fully cover the room.

Solution: Given, Length = 60 m and Width = 40 m

Area of a rectangle = w × h

Area of a rectangle = 60 × 40

Area of the rectangle = 2400 m²

The length of one tile = 1m

The width of one tile = 2 m

Area = w × h

Area of one tile = 1 × 2

Area of one tile = 2 m²

Number of tiles required for covering the floor can be counted by

Area of floor / Area of a tile

2400/2 = 1200 tiles.

6) A square piece of cardboard with an area equal to 36 cm² is cut out from a rectangular piece of cardboard. Find

(a) The length of the square

(b) If the cardboard can be cut into three such squares, find the length, breadth, and area of this rectangular piece of cardboard. 

Solution: (a) Given, The area of the square is 36 cm²

We know that in a square, Area = h².

Therefore, the length of the square = [sqrt{text {Area}}]

Length =[sqrt{36}]

Length= 6 cm

Solution: (b) Given, three squares of length 6 cm can be cut from the cardboard

Therefore, height of the piece of cardboard = 6 cm

Width of the piece of cardboard = 6 + 6 + 6 = 18 cm

Since length = 6 cm and width = 18 cm,

Area = w × h

Area = 6 × 18

Area = 108 cm².