In this platform, you have to learn about how to find the Perimeter and Area of irregular figures. An irregular shape will be of any size and length. We will see irregular shapes all around us, for example, a diamond shape, a kite, a leaf, a flower, etc. The Area of irregular shapes will be the space occupied by the shape which is measured in square units. The Perimeter of irregular shapes is by adding all the lengths of their sides. Any shape whose sides and angles are not of equal length is named an irregular shape.
On this page, you will learn about the definition of the area and the perimeter of irregular figures, how to find the area and perimeter of irregular figures, some solved example problems, and so on.
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Irregular Figures – Definition
The Irregular Figures are defined as a figure that is not a standard geometric shape. An irregular shape is simply a shape where every single side is not the same length. But some irregular figures are made up of two or further standard geometric shapes. If the shape is irregular then it has some angles that are not all the same size. Based on the number of sides or corners we can decide that irregular figure.
How to find Perimeter and Area of Irregular Figures?
The following are the ways for finding the area and perimeter of irregular figures:
How to find Area of Irregular Shapes or Figures?
- Step 1: First, divide the compound shape into a basic regular shape.
- Step 2: Next, find each basic shape area separately.
- Step 3: Now Add all the areas of basic shapes together.
- Step 4: Now, write the final answer in square units.
How to find the Perimeter of Irregular Figures?
To find the perimeter of the irregular figure, we can simply add up each of its outer sides length of a shape. To find the perimeter of any shape like rectangle, square, and so on you have to add all the lengths of four sides. Consider ‘A’ is in this case the length of the rectangle and ‘B’ is the width of the rectangle.
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Perimeter and Area of Irregular Shapes Examples
Example 1:
The Irregular Figure is given below. Find the area of that figure?
Solution:Â
As given in the question, the irregular figure is given.
Now, we can break the given irregular figure. After separating the figure we have two rectangle blocks.
Next, we will find the area of those two rectangles. The area of the irregular figure is the sum of the areas of two rectangles.
The width of one block is 12 and the length of the block is 4.
Next, the width of the other rectangle is 2, but its length is not given. By using the upper rectangle length we can find the length of the lower rectangle. So the right side of the figure is the length of the upper rectangle block plus the length of the lower rectangle block.
Since the total length is 10 units, the right side of the upper rectangle is 4 units long. So the length of the lower rectangle will be 6 units.
So the area of the figure is,
The Area of the figure is the Area of the upper rectangle + Area of the lower rectangle
We know that the Area of the rectangle is, length x width (or) breadth.
So, the area of a figure is , lw + lw = 12(4) + 2(6).
Area of the figure is = 48 + 12 = 60sq.units.
Thus, the total area of the figure is 60 square units.
Example 2:
Find the area of the below-given irregular figure?
Solution:
As given in the question, the given figure is an irregular figure.
Now, we can break the given irregular figure. After separating the figure, we have two blocks one is a triangle block and another one is a rectangle.
Next, we will find the area of the irregular figure. The area of the irregular figure is the sum of the areas of two rectangles.
The rectangle has a length of 8 units and a width of 4 units. We need to find the base and height of the triangle.
On both sides of the rectangle 4units, the perpendicular side of the triangle is 3 units, which is 7- 4 = 3units.
Next, the length of the rectangle is 8units, so the base of the triangle is 3units, which is 8-5= 4units.
Now, we can add the areas then we get the area of the irregular figure.
So, the Area of the figure is the Area of the rectangle + the Area of the triangle.
We know the formulas, the area of the rectangle is, length x width (or) breadth.
The area of the triangle is 1/2bh.
So, the area of a figure is , lw + 1/2bh = 8(4) + 1/2(3)(3).
Area of the figure is = 32 + 4.5 = 36.5sq.units.
Hence, the total area of the given irregular figure is 36.5square units.
Example 3:
The figure is given below. Find the perimeter of the given Pentagon figure?
Solution:Â
As given in the question, the irregular shape figure is given.
This shape is a pentagon because it has five sides. Even though two of its sides are both 13m, it is an irregular pentagon because not all of its sides are the same length.
Now, we have to find the perimeter of the irregular figure.
To find the perimeter of this irregular shape, we add up the five side lengths.
We make the calculation easier by starting with the largest sides and also looking for number bonds to ten.
The two largest sides are 13m and 13m. These add together to make 26m.
The remaining three sides are 2m, 8m, and 9m. Now the value is 2m + 8m+ 9m = 19m.
Now, adding those two values are, 26m + 19m = 45m.
Thus, the perimeter of this given irregular pentagon is 45m.
Example 4:
Find the perimeter of the below-given figure?
Solution:Â
As given in the question, the figure is an irregular figure.
Now, we have to find the perimeter of the irregular figure.
To find the perimeter of this irregular shape, we add up all side lengths.
We make the mathematics easier by starting with the largest sides and also looking for number bonds to ten.
The largest sides is 10 cm. The remaining sides are 2cm, 2cm, 8cm, 8cm and 4 cm. Then the value is 2 cm + 2cm + 8 cm+ 8 cm + 4cm= 24cm.
Now, adding those two values are, 10 cm + 24 cm = 34 cm.
Thus, the perimeter of this given irregular figure is 34 cm.
FAQ’s on Perimeter and Area of Irregular Figures
1. What is meant by Irregular Figures?
An irregular figure is a figure that is not a standard geometric shape. Its area cannot be calculated using any of the standard area formulas. But some irregular figures are made up of two or further standard geometric shapes.
2. Define Area of Irregular Figures?
The area of irregular shapes is defined as the quantity of space that is covered by an irregular shape. Irregular shapes are those shapes that do not have equal sides or equal angles. The unit for the area of an irregular shape is expressed in terms of square units, for representative, m2, cm2, in2, or feet2.
3. How to find the perimeter of Irregular Figures?
In order to calculate the perimeter of an irregular polygon we use the following two steps:
- Step 1: Note the length of each side of the given polygon.
- Step 2: Once the length of all the sides is acquired, then the perimeter is adding all the sides length.