Find the Area & Perimeter of Irregular Shapes- Interesting Worksheet

Area and perimeter are two extremely important concepts in mathematics. We constantly apply formulas of area and perimeter in our everyday lives for instance the size of a house and its floor area, calculating how much wire is needed to fence a field, length and width of wrapping paper for wrapping a present, etc. 

In mathematics, students are taught area and perimeter right from their elementary years to higher classes when they learn about calculus. Hence, having a clear concept of this topic is a boon when it comes to your board exams or other competitive exams like IIT, NEET, etc.

We have mathematical formulas to find the area and perimeter of regular shapes like squares, triangles, rectangles, etc. but when it comes to irregular shapes, it gets a little complicated. But we can always break the irregular shape into two or more regular shapes (squares, rectangles) and then find the area and perimeter of each of those shapes and add all of them to get the figure for the irregular shape. 

The best way to ensure you get good grades in exams is to get your hands on Area of Irregular Shapes Worksheet, which has questions of different kinds for you to practice and master this topic.

Let us learn the difference between regular and irregular shapes and definitions of important terms related to this topic

Area and Perimeter Defined With Examples

• Perimeter – Perimeter comes from the Greek word “Perimetron” where the meaning of “Peri” is “around” and “metron” denotes “measure”. You calculate the perimeter of any shape by either adding the lengths of all the sides of the shape or by measuring the outer boundary of the object or shape. 
• One can easily find the perimeter of small objects by taking a string around the object whose perimeter you are trying to find. Since perimeters are only lengths, their units are also units of lengths like centimetres, meters, etc.
• Example – What is the perimeter for a square when the length of one of its sides is 5 cm?

Solution – Since we know that a square has four sides and all the sides of a square are equal in length, we can calculate the perimeter as;

Perimeter of square = 5 + 5 + 5 + 5 = 20 cm

• Area – The amount of space that any shape, object, or flat surface occupies gives its area. In other words, the total number of unit squares that can fit into a shape defines its actual area. The area of a shape is measured in square units, for example, sq. cm, sq. inches, sq. feet, etc. We can easily understand the concept of area with a solved example discussed below:
• Examples – Find the area of a rectangle given its length and breadth as 12 cm and 3 cm, respectively.

The formula for area of a rectangle = length * breadth = 12 * 3 = 36 sq. cm.

Difference Between Regular and Irregular Shapes

• A regular shape is one that has all its sides of the same length, and all the interior angles (inside angles) are equal.
• An irregular shape is any shape where the sides of the shape have unequal lengths, and all the angles are not equal. 

Common Examples of Irregular Shapes in Daily Life

Some of the objects in daily life that have an irregular shape are stars, moon, etc.

• Look at the staircase of any building and think about its surface. The surface area of a staircase consists of polygons like rectangles and squares.
• A leaf of any plant has an irregular shape.
• A school’s playground which has a running track is an irregular shape made up of regular shapes.

Finding The Area of An Irregular Shape

You can easily find out the area of an irregular shape if you understand how to divide the given irregular shape into familiar regular shapes accurately. Let us look at the irregular shape shown below:

• This shape can be split into polygons, as marked by P, Q, R, S, T, U. These polygons are joined to give the final irregular figure.

• We can then find the area of individual polygons and then add them up to give the total area of the figure.

Different Methods For Finding Areas of Irregular Shapes

Since we do not have a direct formula for calculating area, we employ different methods for achieving our goal. There are a couple of ways of finding areas of irregular figures. 

• Method 1 – By decomposing the irregular shape into squares and rectangles. This is discussed in the above example. We will consider another figure displayed below:

Area of the shape = Area of triangles A, B, D, E, G + Area of square C + Area of quadrilateral F.

• Method 2 – Square units or grid method – In this method, we divide the shape into tiny unit grids or squares. The total number of unit squares that fall inside the shape whose area we have to find out determines the area of the shape. 
• The square is counted as “1” if more than half of the square falls within the shape. Let us consider an irregular shape of a leaf and use this method to find the area

So all the unit squares that are within the leaf give us its total area, which in this case is 39 sq. cm.

Finding Perimeter of an Irregular Figure

Now we will apply the same mechanism of separating an irregular figure to find its perimeter. Consider the below shape:

To calculate its perimeter, you sum the lengths of each side. Hence its perimeter = 9 cm + 11 cm + 5 cm + 97 cm  = 32 cm.

Conclusion

FInding area of an irregular shape is all about dividing or decomposing the irregular figure into known shapes. Once you can successfully do that, you just have to find the area of each part by applying the formula for that shape and then add them all up. For shapes that can not be divided into known shapes like squares, rectangles, and triangles, we can apply the units of the square method.