In geometry, irregular and regular polygons are also referred to as irregular and regular shapes. These polygons differ from one another in terms of their dimensions. Polygons are two-dimensional closed shapes where all sides are connected. The sides of a polygon are called edges, and the point where two sides meet is the vertex.
Having said that, an irregular shape has unequal sides and angles, which are unequal in measure. Some examples of irregular shapes are irregular hexagons, irregular pentagons, parallelograms, isosceles triangles, and more.
Here, we will talk about the method of Area of Irregular Shapes Calculation.
Irregular Properties: Polygons
There are certain properties of irregular polygons that set them apart from other kinds of polygons. These are as follows,
- An irregular polygon has unequal angles and sides.
- An irregular polygon can be concave or convex.
- An irregular polygon has a complex shape.
- An irregular polygon can be infinitely large as its side are unequal in length.
- Quadrilaterals, trapeziums, parallelograms are called irregular polygons or shapes as their adjacent angles, and adjacent shapes are unequal.
Area of Irregular Shapes
The amount of the region that is covered by an irregular shape is called its area. Irregular shapes neither have equal angles or sides. Hence, to determine an irregular shape’s formula, it can be divided or decomposed into multiple familiar shapes. Then the area of these multiple familiar shapes can be added for determining the total area.
There are different types of irregular shapes that we can see every day in our lives:
- A plant’s leaf is an example of an irregular shape.
- A school’s playground with a running track has an irregular shape.
- The staircase of your building or house is an irregular shape made of polygons like squares and rectangles.
The unit of measurement of the area of irregular shapes is expressed as ft2, in2, cm2, and m2.
How to Calculate the Area of Irregular Shapes?
Calculating the area of irregular shapes depends on the method of decomposing the irregular shape into more familiar shapes. When you have to find the area of an irregular figure, you have first to split it into different polygons.
After decomposing, you can calculate the area of all the polygons and add them together to determine the area of the irregular shape.
The formula for Finding the Area
There is not a single formula that you can use for calculating the area of irregular shapes. There are various methods that you can use depending on the individual problem that you are solving. However, the two most commonly used methods are,
- Method 1: The area of irregular shapes can be calculated by dividing the irregular shape into similar polygons and finding the area of each of those polygons.
Hence, the area of the irregular shape=area of the polygons found in the shape.
⇒ The area of the irregular shape = area of G + area of F + area of E + area of D + area of C + area of B + area of A.
- Method 2: The irregular shape can be divided into smaller unit grids or squares depending on the problem. The total quantity of these unit grids or squares that fall within the shape decides the total area.
Hence, while calculating the area into a more accurate estimation, a shaded region is considered “1 square” if it covers over one-half of the square. Therefore, this method can be used for determining the area of those irregular shapes that have curves.
Hence, the area of an irregular shape = total unit squares that are falling under that irregular shape.
Example of Finding the Area of an Irregular Shape
Question 1: What is the area of the irregular shape given below?
To calculate the area of the above-mentioned irregular shape, you would have to add up the area of the individual shapes that connect to create this irregular shape.
Therefore, let’s find their area first:
- Area of the semicircle (Q) ⇒ πr2/2 ⇒ (3.14×52)/2 (the diameter is considered as 10 by applying the Pythagoras theory for triangle R) ⇒ area of Q = 39.25 square units.
- Area of rectangle (P) ⇒ width x length ⇒ 8×6 = 48 square units.
- Area of triangle (R) ⇒ ½ x height x base ⇒ area of R = ½ x 6 x 8 = 24 square units.
- Area of rectangle (S) ⇒ breadth x length = 8 x 6 = 48 square units
The next step is to calculate the irregular shape’s area through the area of the decomposed regular shapes.
Hence, area of the irregular shape = area of P + area of Q + area of R + area of S
⇒ 48 + 39.2 + 24 + 48 = 159.25 square units.
Therefore, 159.25 square units are the area of the irregular shape.
An irregular shape or polygon can be of any length and size. Hence, the area of such shapes or polygons is calculated by decomposing the shape into multiple regular shapes.