Area of Irregular Shapes

Dhristi JEE 2022-24

Irregular shapes

Irregular Shapes are Polygons with five or more sides of varying lengths. These Shapes or figures can be decomposed further into known Shapes like triangles, Squares, and Quadrilaterals to evaluate the Area.


Some examples of Irregular Shapes are as follows:


Daily Life Objects with Irregular Shapes



How to calculate the Area of Irregular Shape?

Finding the Area of Irregular Shapes

Different methods for estimating the Area of Irregular Shape are:


  • Evaluating Area using unit Squares.

  • Dividing the Irregular Shape into two or more Regular Shapes.

  • Dividing the Irregular Shape with curves into two or more Regular Shapes.


How to Find the Area of an Uneven Shape?

Evaluating Area Using Unit Squares

We can use this method for Shapes with curves apart from perfect circle or semicircles and Irregular Quadrilaterals. In this method, we first divide the Shape into unit Squares. The total number of unit Squares falling within the Shape is used to determine the total Area.



For Example: Calculate the Area by counting the unit Squares in the given below figure


Ans: If we denote each unit Square in centimetre, the Area will be 6 cm2.


To Calculate the Area of an Irregular Shape with Curved Edges

Dividing the Irregular Shape Into Two or More Regular Shapes

Use this method to calculate the Area of Irregular Shapes, which are a combination of triangles and Polygons. Using predefined formulas calculate the Area of such Shapes and add them together to obtain the total Area.


For example, in the given below Irregular Shape, we will divide multiple edges into a triangle and three Polygons.



The total Area of the figure can be calculated by adding individual Area:


Total Area = Area (ABIM) + Area (BCGH) + Area (CDEF) + Area (JKL)

⇒ Total Area = (AB × BI) + (BC × CG) + (CD × DE) + (12 × LJ × KO)

⇒Total Area = ( 10 × 5) + (3 × 3) + (2 × 2) + (1⁄2× 4 × 4)

⇒ Total Area = 50 + 9 + 4 + 8

⇒ Total Area = 71 cm2


Calculating the Area of an Irregular Shape

To calculate the Area of Irregular Shapes, divide the Shape with curves into two or more Regular Shapes.


In this method, divide an Irregular Shape into multiple Squares, triangles, or other Quadrilaterals. Depending on the Shape or curves, a part of the figure can be a circle, semicircle or quadrant as well.


Find the are of a given Irregular Shape with 8 sides, including one curve.


Solution: We will determine the unknown quantities by the given dimensions for the sides. First, we need to divide the figure into two rectangles and a semicircle.



The Area of the Shape ABCDEF is:

Total Area (ABCDEF) = Area (ABCG) + Area (GDEF) + Area (aob)

Total Area = (AB × AG) + (GD × DE) + (1⁄2 × π × ob2)

Total Area = (3 × 4) + (10 × 4) + (1⁄2 × 3.14 × 12)

Total Area = 12 + 40 + 1.57

Hence total Area = 53.57 cm2


How to Find the Area of Irregular Shapes Using Graph Paper?

What is the Area of Irregular surface?


Find the Area of a given leaf.



Solution: To find the Area of the Irregular surface in the above case leaf we have to put the leaf on graph paper and draw its boundary.





The Shape of a leaf is Irregular. So we will assume that more than half of the Square covered by leaf will be counted as 1 and less than that will be counted as 0.



Now count the number of fully covered Shapes. There are 64 Squares fully covered.



Also, count the partially more than half covered Squares and each will count qs 1 Square. There are 17 Square more than half Square.



Also, count the partially less than half covered Square and each will count as 0. There are 16 Squares less than half Square.


Now add all the Squares to find the Area of leaf = 64 + 17 x 1 + 16 x 0 = 64 + 17 = 81 sq. units.


Hence the Area of the leaf will be 81 sq. units.


Area of Irregular Shapes Formula

To find the Area of Irregular Shapes, first, we need to divide the Irregular Shape into Regular Shapes that you can recognize such as triangles, rectangles, circles, Squares and so forth.


Then, find the Area of these individual Shapes and add them to get an Area of Irregular Shapes.


Solved Example

Q. Find the Area of the given Shape?



Solution: The figure above has three Regular Shapes. Start dividing from the top, it has a triangle, a rectangle, and a trapezoid.


We will find the Area for each of those three Shapes and add the results to get the final Area of a figure.


Triangle

Area of triangle = (base × height)/2

= (3 × 4)/2

= 12/2

= 6

Rectangle

Area of rectangle = length × width

= 3 × 10

= 30

Trapezoid

Area of trapezoid = ((b1 + b2) × h)/2

= ((3 + 5) × 2)/2

= (8) × 2/2

= 16/2

= 8

Hence Area of the given Shape = 6 + 30 + 8 = 44.


Irregular Shapes

The space occupied by Shape is known as the Area of Irregular Shape; it is measured in Square units. The size and length of Irregular Shapes can be of any measurement. There are various Irregular Shapes that we can see around us like kites, leaves, diamonds, etc. Therefore Irregular Shapes are any Shapes whose angles and lengths are not equal. Students can study Areas of Irregular Shapes with Vedantu's subject experts who guide learners to understand each and every topic so that it will be easier to learn and score good marks.


More into Irregular Shapes

The amount of region covered by that Shape is known as the Area of Irregular Shapes. The sides and angles of Irregular Shapes are different. to find the Area of Irregular Shape we have to decompose it or divide it into multiple known Shapes and then the Area of those Shapes will be added to get the total Area of Irregular Shape. Irregular Shapes can be seen everywhere around us in our daily life for example:


  • The staircase of a building is composed of Polygons like rectangles and Squares, the surface Area of the staircase is an Irregular Shape.

  • The school’s playground that has a running track is an Irregular Shape which is the combination of Regular Shapes.

  • The leaf of a tree or plant is of Irregular Shape. Etc.


Unit Area of an Irregular Shape can be expressed in m2, cm2,in2 or ft2. 


Steps to Find the Area of Irregular Shapes

Step 1 - Area of Irregular Shape is to be found by decomposing the Irregular Shapes into familiar Shapes.

Step 2 - Students should know the way to decompose Irregular Shapes.

Step 3 -  dividing the Irregular Shape into different familiars Shapes and finding the Area of familiar Shapes

Step 4 - Now add all the Areas of the familiar Shapes to know the Area of the Irregular Shape.


The #1online learning portal Vedantu provide students complete guide to studying the topics like Area of Irregular Shapes - Calculation, Examples, etc. students can easily download the Free PDF and prepare for their exams they can rely on the study material as it is 100% accurate and is according to the latest guideline and syllabus.

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FAQs (Frequently Asked Questions)

1. How Do You Find the Area of Irregular Shapes?

To find the Area of Irregular Shapes, first we need to divide the Irregular Shape into Regular Shapes that you can recognize such as triangles, rectangles, circles, Squares etc. Then, find the Area of these individual Shapes and add them up to get the Area of Irregular Shapes. Students can understand the concept well with the revision notes provided by Vedantu that have described the concepts in detail to help the student to gain complete knowledge, so that they can solve any type of question-based on the given topic.

2. What are Irregular Shapes?

An Irregular Shape doesn't have equal sides or equal angles. Irregular Shapes can be seen everywhere around us like stars, diamonds, leaves, stairs, etc. Students can study the concept of Irregular Shapes by understanding the formation of that Shape. Students need to decompose and divide the Irregular Shapes into some Regular familiar Shapes so that their Area can be calculated and by adding them we can calculate the Area of Irregular Shapes. Calculation of the Area of Irregular Shapes is not easy, it is a bit complicated and you need to practice and learn all the formulas to get answers in one go.

3. What are the Applications of the Irregular Shapes Calculation Formula?

The formula used to estimate Area for Irregular figures is an essential method for drawing maps, building architecture, and marking agricultural fields. We can also apply the concept in the cutting of fabrics as per the given design. To study the given Shapes, students need to get complete knowledge about the different figures and the formulas to calculate the Area of all the Shapes. With practice, students can excel in solving the questions based on these topics and they will also gain knowledge about how to decompose an Irregular Shape and apply the formulas to it.

4. How is the Area of Irregular Shapes different from Regular Shapes?

One of the most important topics of the syllabus is Regular and Irregular Shapes and students should know the Difference between Regular Shapes and Irregular Shapes, here are some of the differences between the two:

  • The Regular Shape has equal sides and angles, but in an Irregular Shape, the sides and angles are different from each other. 

  • The Area of a Regular Shape can be determined by easily applying a suitable formula to it, but in order to find the Area of Irregular Shape, we need to decompose it into multiple Regular Shapes and then add the Areas of all the Regular Shapes.

5. Where can I get the best study material for getting complete knowledge of Irregular Shapes, Area, calculation, and examples?

Vedantu is the best online learning app that helps students to get free study material for all the topics they require to study. Students can download a free PDF for Irregular Shapes that covers everything about Irregular Shapes like Area of Irregular Shapes, calculation, and examples of Irregular Shapes. Students can prepare this topic well by solving the important questions provided by Vedantu's expert which provides practical knowledge about how to apply formulas to determine the Area of various Irregular Shapes.

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