How to get area of irregular shape

Some irregular figures are made of rectangular or square regions. The areas of such irregular figures can be determined by calculating the areas of these rectangles and squares.

To find the area of a figure which is a combination of rectangles and a squares, we calculate the area of each figure separately and then add them to find total area.

Solved examples to find areas of irregular figures:

1. Find the area of the given figure:

Solution:

Area of a rectangle ABDC = 3 × 1

                                     = 3 sq. cm.

Area of a rectangle EFGD = 2 × 1

                                     = 2 sq. cm.

Therefore, Total Area = 3 + 2

                               = 5 sq. cm.

Area of the given figure = 5 sq. cm.

2. Find the area of the following figures.

Solution: 

Area of the rectangle PQTU = 5 × 3 = 15 sq. cm.

Area of the square VRST = 2 × 2 = 4 sq. cm.

Total area of the figure = 15 + 4 = 19 sq. cm.

3. Find the area of the following figure.

Total area = Area of the rectangle ABGF + Area of the rectangle CDEG

               = 8 × 2 cm\(^{2}\) + 2 × (8 - 2) cm\(^{2}\)

               = 16 sq cm\(^{2}\) + 2 × 6 cm\(^{2}\)                

               = (16 + 12) cm\(^{2}\)

               = 28 cm\(^{2}\)

Therefore, area of the figure = 28 cm\(^{2}\)

4. Find the area of the following figure.

(i) We divide the figure into two parts.

PQRS is a rectangle of length 9 cm and breadth 5 cm.

Area of PQRS = 9 × 5

                    = 45 sq. cm

STUV is a square of side 3 cm

Area of square STUV = 3 × 3 = 9 sq. cm

Hence, total area of the figure = 45 + 9 = 54 sq. cm

5. Find the area of the figure given on the right side.

Total area = Area of the rectangle ABKL + Area of the rectangle EFGH + Area of the rectangle CDIJ

                = 20 × 4 cm\(^{2}\) + 20 × 4 cm\(^{2}\) + 8 × 4 cm\(^{2}\)

                = 80 cm\(^{2}\) + 80 cm\(^{2}\) + 32 cm\(^{2}\)

                = (80 + 80 + 32) cm\(^{2}\)

                = 192 cm\(^{2}\)

Therefore, area of the figure = 192 cm\(^{2}\)

6. Find the area of the following figure.

Figure QTUV is a rectangle of length (5 cm + 5 cm = 10 cm) and breadth 2 cm

Area of QTUV = 10 × 2

                    = 20 sq. cm

PQRS is a square of side 5 cm

Area of PQRS = 5 × 5 = 25 sq. cm

Hence, total area of the figure = 20 + 25

                                            = 45 sq. cm

● Area.

Area of a Rectangle.

Area of a Square.

To find Area of a Rectangle when Length and Breadth are of Different Units.

To find Length or Breadth when Area of a Rectangle is given.

Areas of Irregular Figures.

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To find the Number of Bricks or Tiles when Area of Path and Brick is given.

Worksheet on Area.

Worksheet on Area of a Square and Rectangle

Practice Test on Area.

5th Grade Geometry

5th Grade Math Problems

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Before learning about the area of irregular shapes, let’s recall what irregular shapes are and the various irregular shapes around us. Irregular shapes are those shapes that do not have equal sides and angles. A kite, leaf, flower, etc., are examples of irregular shapes around us. The area of these types of irregular shapes can be determined by dividing the shape into small regular polygons. In this article, you will learn the methods of finding the area of irregular shapes, along with the graphical illustration.

Learn more about shapes here.

What is the Area of Irregular Shapes?

As mentioned above, irregular shapes are those shapes that do not have equal sides or equal angles. The area of an irregular shape is the entire region covered by that shape on a two-dimensional plane. To find the area of an irregular shape, it can be divided into multiple familiar shapes, such as triangles, squares, and rectangles. Then, we can get the total area by adding the area of those smaller shapes. Also, the area of irregular shapes can be expressed in different units such as cm2, ft2, m2, etc.

Learn: Area

How to Find the Area of Irregular Shapes?

Finding the area of irregular shapes is not as easy as it is for regular shapes or polygons. However, there are different methods to estimate the area of any irregular shape. Here, you will learn two important methods of finding the area of given irregular shapes. They are:

• Dividing the shape into possible regular polygons
• Using the graph paper

Read more:

• Area of polygon
• Regular and Irregular polygons
• Area of shapes

Let’s learn how we can estimate the area of irregular shapes using the decomposition of the shape into smaller polygons.

Calculating the Area using Decomposition of an Irregular Shape

Consider an irregular shape as given below:

The area of this irregular shape cannot be calculated using a single formula. Thus, we need to decompose the shape into possible simple polygons such as triangles, squares, and so on. This can be done as shown below:

Therefore, the decomposed shape contains a parallelogram, rectangle, square and triangle. So, the area of the above irregular shape can be calculated as:

Area of the shape = Area of parallelogram + Area of rectangle + Area of square + Area of triangle

Area of Irregular Shapes Using Graph Paper

Let’s learn how to find the area of irregular shapes using graph paper with the help of an example.

If the shape is given on graph paper, we can directly count the number of squares covered by that shape. Otherwise, we need to draw the graph lines or square grids over the given irregular shape.

Go through the example given below to understand this method of finding the area of an irregular shape in a better way.

Example of Area of Irregular Shapes by Counting Squares

Question:

Find the area of the shape in square units.

Solution:

Let us count the squares that are completely covered, half covered and so on. Also, these can be marked as shown below:

Now, we need to write the number of squares that are covered by the shape.

Number assigned for covered portions

Portions of squares covered

Total

1

Fully covered squares

7

2

Half covered squares

0

3

More than half covered squares

7

4

Less than half covered squares

8

For fully covered square grids, we can take 1 square unit for each.

For half-covered squares, we should assign ½ square units for each.

If the square is covered more than half the portion, then assign 1 square unit for each such portion.

If the square grid is covered less than half, then assign 0 square units for each such portion.

Therefore, the area of the given shape = 7(1) + 0(½) + 7(1) + 8(0)

= 7 + 0 + 7 + 0

= 14

Hence, the area of the given irregular shape is 14 square units.

Similarly, we can find the area of irregular shapes given on graph paper. We can also draw the square grids, if it is not given on the graph paper.

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