Introduction
Mathematics is one of the vital organs of science in today's time. Mathematics involves various genres of calculations and Measurements turn out to be the most productive parts of it, which is essential in our day-to-day life. In Mathematics, with we image of a plane figure, we define it by its boundaries, forms, and boundaries. Every figure needs a measure of comparison, may it be size or area. Here the area dives in as an essential factor to measure the space occupied by an object lying on a plane surface. Therefore, the area of a figure is defined by measuring the surface enclosed by a closed figure.
There numerous shapes and figures such as a rectangle, square, circle, etc. In this article, we will principally be specializing in the understanding of the Area of Rectangle Formula. The rectangle is an equiangular quadrilateral whose opposite sides are equal. Squares have opposite sides equal in length, and we can also consider them as a rectangle. The rectangle is the same as a parallelogram, displaying two equal and opposing sides parallel to each other. Let's dive in to find the area of rectangle, and we will also highlight some critical questions and their solutions to make the topic crystal clear to the readers.
What is the Area of Rectangle?
Before knowing the meaning of Area of rectangle and Area of Rectangle Formula, let's get a glimpse of 'What is a rectangle?'
In simple words, a Rectangle is just a quadrilateral, having four sides. Rectangles comprise four lines as their sides. Every other side of the rectangle is parallel to each other, highlighting the rectangle as a parallelogram. Containing four sides, the rectangle also incorporates four angles in itself; each angle is a right angle, i.e., at 90 degrees to each other. Therefore an equiangular rectangle includes four angles, all at 90 degrees to each other. The rectangles depict another property of having two diagonals of equal lengths. A diagonal can be defined as a path or a straight line that joins the alternate corners or vertices within the rectangle. This property portrays the two diagonals of a rectangle as congruent.
Now, let's find out the actual meaning of the Area of Rectangle.
The area is termed as a quantity that portrays the extent of a two-dimensional shape or planar lamina or a specific figure. The standard unit for the area according to International Standard Units is square (expressed as m²). If we take a solid figure like a sphere, cone, or cylinder, its boundary surface area is known as the surface area.
A rectangle is a 2-dimensional figure containing four sides and four vertices and thus possess four angles. All of these angles are 90 degrees to each other. The rectangle resembles a parallelogram as it also has opposite sides equal and precisely parallel to each other. The only point of difference between them is that the parallelogram does not comprise all angles 90 degrees to each other. The Area of the Rectangle relies upon the four sides of the rectangle.
We can depict the rectangle formula's area as the product of the respective rectangle's length and breadth. Another method to measure the rectangle is by calculating its perimeter, which is another basic rectangle formula. As it is highlighted by the summation of the rectangle's sides, it turns out to be one of the essential properties. But if we notice a square contain all sides equal. The area of a square can be calculated by squaring the length of the sides of it. Similarly, if we take a circle, its area is pi times of the square of its radius.
Table of Content
- Area of Rectangle Formula
- How to Calculate the Area of Rectangle
- Area of Rectangle Problems With Solutions
- Frequently Asked Questions( FAQs)
Area of Rectangle Formula
The Area of Rectangle or any polygon is the space that it occupies or encloses within. It can be defined as the number of the square units with the specific polygon—and being a two-dimensional property, the area possesses both length and breadth. A figure's area can be measured using particular units such as square feet, square meters, or square inches. In contrast, the area of larger shapes is measured in square kilometers, square hectares, or acres. Therefore, we can grasp any of the two methods to calculate the size of any object. Let's take an example, so employing the formula of the area, we can easily calculate the depth of a lake or a building's size.
Accordingly, we can calculate the area of the rectangle in square units by multiplying its length and width. In contrast, the lateral and surface areas can only be calculated in the case of three-dimensional figures. And these options are not available for rectangle as it is a two-dimensional figure. We can only estimate the perimeter and area of a rectangle.
So, let's find the Area of Rectangle Formula and deal with some of the complicated questions.
The Area of Rectangle Formula
Area of a Rectangle
A = l × b
So, the above Area of Rectangle Formula highlights that we can easily calculate the Area of Rectangle once we grab the respective rectangle's length and width. The product of the rectangle's length and breadth depicts the Area of Rectangle in square unit dimension. But if we consider a square, the product of the sides will result in its area. The main point of difference between the rectangle and square is the length and width of a rectangle are different, whereas, in a square, all of its sides are equal.
Therefore, we can easily highlight the Area of Rectangle as the width of the rectangle time height.
For instance, let's say a rectangle has a 10-meter width and 5-meter height.
Therefore by applying the Area of Rectangle Formula, we get
Area of Rectangle = width x height
Area = 10 m x 5 m
Therefore, the area of the rectangle = 50 m²
Now, in the case of a square, all of its sides are equal. The formula of Area changes from area = Width x Height
To, Area = Side x Side, i.e. Area = h x h, Area = h²
Therefore, in the case of a square, the area can be calculated by squaring its sides.
How to Calculate the Area of Rectangle
There is a bucket full of formulas to calculate simple figures such as rectangle, circle, triangle, etc. We can efficiently utilize these formulas to produce the area of any polygon. But for figures with curved boundaries, usually, calculus is implemented to find the area.
The area plays a significant role in modern mathematics. In addition to its vitalities in pure mathematics and calculus, it is also used for linear algebra determinants. It also defines the primary properties of surfaces in differential geometry. The area can also be outlined as the employment of axioms, highlighting it as a function of a bunch of specific plane shapes to the set of real numbers.
Here are the steps to find the Area of Rectangle –
- Step 1 – Collect the Length and Width of the Rectangle from the provided set of information.
- Step 2 – Apply the Area of Rectangle Formula.
- Step 3 – Multiply the Length and Breadth of the Rectangle.
- Step 4 – Collect the results and write the output in square units.
Let's take an example to find the Area of Rectangle, using formula –
Let's say a rectangle has 6-meter width and 3-meter length.
Now, we have length = 3m and Width = 6m
Applying the Area of Rectangle Formula, Area = L x W
Therefore, Area = 3 x 6
i.e., Area = 18 m² (Answer)
You may be curious why we use length x width as the Area of Rectangle. So, let's explore this,
The diagonals of a rectangle are separated into two equivalent right-angled triangles. So, we can now get the area of the rectangle by adding the sum of the areas of both the triangles.
Suppose WXYZ is a rectangle.
Now, suppose diagonal WY divides the rectangle into two halves, i.e., ∆WXY and WZY.
Now ∆WXY and ∆WZY are displayed as congruent triangles.
Area of ∆WXY = ½ x base x height = ½ x XY x WX = ½ x b x l
Area of ∆ADC = ½ x base x height = ½ x ZY x WZ = ½ x b x l
Area of rectangle WXYZ = Area of ∆WXY + Area of ∆WZY
Area (WXYZ) = 2(½ x b x l)
Area (WXYZ) = l x b
Therefore, the area of rectangle = Length x Breadth, or, Length x Width.
So, here we are with the complete procedure to find the Area of Rectangle.
Area of Rectangle Problems with Solutions
Now that we have a glimpse of the concepts of the Area of Rectangle, let's jump into the questions and solutions of the topic to enhance your understanding –
Q: Given Information - The length of a rectangle is 15 cm, and the width is 4 cm. Calculate the area of the rectangle.
Ans: Given, Length of the rectangle = 15 cm, Width of the rectangle = 4 cm
Now, Applying Area of Rectangle Formula,
We get Area of a rectangle = Length × Width.
Therefore, Area = 15 × 4 = 60
So, area of rectangle = 60 cm2
Q: Given Information - length and the breadth of a rectangular piece of the plot are 600 m and 200 m, respectively. Calculate its area. Then, calculate the cost of painting the sheet if it costs 60 paise to paint one square meter area.
Ans: Area of a rectangle = L x B, where L is the length and B is the rectangle's breadths.
As given in the problem, L = 600 m and B = 200 m.
Therefore, Area of the rectangle A = 600 m x 200 m = 1, 20,000 square meters.
Now, let us find the cost of painting the land.
Cost of the painting of an area of 1 square meter = Re 0.60
So, the cost of painting the total area of the rectangular land = 0.60 x 120000 = Rs 72000
Q: Given Information - The area of a rectangular sheet is 500 cm². If the length of the sheet is 25m, calculate its width.
Ans: According to the problem, the Area of the rectangular sheet = 1000 cm² and the Length (L) =50 cm
As we know, the area of the rectangle = L × B, here B = width of the sheet, L = Length of the sheet)
So, width B = (Area/L)
Therefore, Width B = (1000/50) = 20 cm
Q: Given Information – A floor with a length and width of 50 m and 40 m respectively needs to be coated with rectangular tiles. Every tile dimension is 1 m x 2 m; calculate the total number of tiles required to cover the floor.
Ans: Given, Length of the floor = 50 m, breadth of the floor = 40 m
Applying Area of Rectangle Formula,
We get, Area of the floor = length x breadth = 50 m x 40 m = 2000 square meter
Length of one tile = 2 m
The breadth of one tile = 1 m
Therefore, Area of one tile = length x breadth = 2 m x 1 m = 2 sq. m
Number of tiles, we will need = area of floor/area of a tile = 2000/2 = 1000 tiles
Q: Given Information - The length and breadth of a rectangular blackboard are 120 cm and 100 cm; calculate the blackboard area.
Ans: Given, Length of the blackboard = 120 cm = 1.2 m, Breadth of the blackboard = 100 cm = 1 m
Applying Area of Rectangle Formula,
We get, Area of the blackboard = area of a rectangle = length x breadth = 1.2 m x 1 m = 1.2 square meters.
So, here are some questions related to the topic. You can grab many more questions ranging from easy to complex on the internet to polish your understanding of the concepts.
Frequently Asked Questions
Q1: What is the Area of Rectangle?
Ans - There are many formulas to find the area of simple figures such as square, rectangle, circle, triangle, etc. We can easily use these formulas to grab the area of any specific 2-dimensional polygon. But while dealing with figures with curved boundaries, we usually use calculus to find the area. The area plays a vital role in modern mathematics.
The Area of Rectangle is the space that it occupies or encloses within. In simple words, the Area of Rectangle is the space occupied by it on a two-dimensional plane. A rectangle is a 2-dimensional figure containing four sides and four vertices and thus includes four angles.
Q2: What is the Perimeter of Rectangle?
Ans – The perimeter of a rectangle can be outlined as the summation of all the sides of the rectangle. For any specific polygon, the perimeter's formula represents the total distance along its sides. If we take the rectangle's case, as the opposite sides of a rectangle are equal, the rectangle's perimeter can be presented as the sum of the twice of width plus double length. The perimeter of any figure is denied by 'p.'
The formula of Perimeter of Rectangle = 2(L+W), here L = Length of one side of the rectangle, W = Breadth of a side of the rectangle).
Q3: What is the Area of Rectangle Formula?
Ans - Area of a Rectangle
Area = L × B (Here L = Length of rectangle, B = Breadth of rectangle)
So, the above Area of Rectangle Formula portrays that one can easily find the Area of Rectangle once we collect the respective length and width. The product of the rectangle's length and breadth presents the Area of Rectangle in square unit dimension. But if we take the case of a square, the product of the sides will result in it's the area of the square. The main point of contrast between the rectangle and square is the length and breadth of a rectangle are different, while, in a square, all of its sides are equal.
Q4: What do you mean by Unit Area?
Ans – According to the International System of Units, any figure's unit area is a square unit. We can present the standard unit area as square meters (it is the area of a square with sides 1 meter long)—for instance, m² or sq.m.
Q5: What is Square Unit?
Ans – According to the International System of Units, a square unit can be defined as a square with sides of 1-meter length. We can also present the square unit in the Cartesian Plane with corners in four points (0, 0), (1, 0), (0, 1), and (1, 1). Therefore, any figure with an area of two square meters will have the same area as the area of two such squares. In pure mathematics, we can define a square unit to have one as an Area and presents the area of any other figure or surface as dimensionless real numbers.
Q6: Why the Area of the Rectangle is Length multiplied by the width of the rectangle?
Ans - Let's see why the Area of Rectangle Formulas is depicted by Length x Width –
Suppose we have a rectangle ABCD
Now, suppose diagonal Ac divides the rectangle into two halves, i.e., ∆ABC and ADC.
∆ABC and ∆ADC are now congruent triangles.
Area of ∆ABC = ½ x base x height = ½ x AB x AC = ½ x b x l
Area of ∆ADC = ½ x base x height = ½ x DC x DA = ½ x b x l
Then we get Area of ABCD = Area of ∆ABC + Area of ∆ADC.
Area (ABCD) = 2(½ x b x l)
Area (ABCD) = l x b
Now we get the area of rectangle = Length x Breadth, or, Length x Width.
Q7: Why we need to find the area of a figure?
Ans – Area is one of the mathematical terms used to define the space occupied or enclosed by an object in a two-dimensional plane. The calculation of area is vital as it plays a crucial role in day-to-day life too. For instance, let's say you may want to paint the wall of your room. And now, you must calculate the area of the wall first to know how much paint you will require. Or let's say you want to sow grass seed in a piece of land. Here, you must also see using the area formula to define how much grass seed can be utilized.
Q8: Who discovered the Area of Rectangle?
Ans – The concept of Area of Rectangle, or the theory of area, was introduced by Egyptians and Mesopotamians. Area refers to a quantity that highlights the extent of a two-dimensional shape or specific figure. The standard unit for the area following International Standard Units is square (expressed as m²). For a solid figure like a sphere, cone, or cylinder, the area of its boundary surface is quoted as surface area.
Q9: Define Area of the Shaded Region?
Ans – We can define the area of the shaded region as the difference between the Area of the complete polygon and the Area of unshaded parts of the polygon. The area of the shaded part of a polygon may be present at the center of the figure or on one of its sides. Generally, we find the area of shaded parts in either of these two regions.
Q10: If a box has every side rectangle with a length of 10 cm, a width of 6 cm, and a height of 8 cm. Find the total area of the box?
Ans - As the sides, a pair of the box are equal.
Therefore, the two of the sides possess edges of 10 cm and 6 cm.
So, their area is (10 × 6) × 2 = 60 × 2 = 120 cm2
Again, two of the sides have edges of 10 cm and 8 cm.
Therefore, area will be (10 × 8) × 2 = 80 × 2 = 160 cm2
Again, two of the sides have edges of 8 cm and 6 cm.
Therefore area will be (8 × 6) × 2 = 48 × 2 = 96 cm2
Now the total area will be 120 + 160 + 96 = 376 cm2