Learn How to Measure The Area of Irregular Shapes

Key concepts

• How to break larger area into smaller areas
• Divide the irregular shape into squares and rectangles
• Find the area of each individual squares and rectangles
• Find the area of any irregular shapes

1.1 Area of Square

1. All sides are of equal length in a square.
2. Area of a square = Side x Side
3. Side = 6 inches
4. Area = 6 in x 6 in. = 36 square inches

1.2 Area of Rectangle

As the opposite sides are the same in a rectangle area

Area of the rectangle = Length * Width

Length = 8 inches, Width = 5 inches

Area = 8 in x 5 in = 40 square inches

Jack wants to lay artificial grass for playing golf in the ground. Let us help Jack find the area of the ground to be covered by grass.

Method 1

Draw the figure on the grid paper and count the unit squares covered to find the area.

Total number of squares = 56

Area to be covered by grass = 56 square feet

Method 2

• Break the larger area into smaller parts.
• Look for the possibilities in which the smaller shapes are part of a larger shape.
• Divide the larger area into smaller rectangles and find the area.

The golf area to be covered by grass is divided into rectangles A, B and C

Find individual areas

Area of rectangle A = 4 ft x 3 ft = 12 square feet

Area of rectangle B = 4 ft x 3 ft = 12 square feet

Area of rectangle C = 4 ft x 8 ft = 32 square feet

Total area = 12 + 12 + 32 = 56 square feet

 Steps to find the area of  an irregular  shape

1. Find all the unknown sides.
2. Divide the irregular shape into squares and rectangles
3. Find the area of each individual squares and rectangles
4. Add all the individual areas to find the total area of the irregular shape.
   Total area = sum of all individual areas

  Steps to find the area of an irregular  shape

1. Find all the unknown sides.

In this example, find the values of side a and side b

Side a = 10 – 3 = 7 cm

Side b = 5 – 3 = 2 cm

2. Divide the irregular shape into squares and rectangles

In the example, the figure is divided into one rectangle-A and one square-B 

Total area = Area of Rectangle A + Area of Square B

Steps to find the area of an irregular shape

3. Find the area of each individual squares and rectangles

Area of rectangle A = length x width

= 10 x 2 = 20 square cm

Area of square B = side x side

= 3 x 3 = 9 square cm

4. Add all the individual areas to find the total area of the irregular shape

Total area = Area of rectangle A + Area of rectangle B

= 20 sq. cm + 9 sq. cm

= 29 sq. cm

Example: Find the area of the shaded part

Total area of the shaded part = Area of the outer rectangle – Area of the inner rectangle

Area of outer rectangle = 10 cm x 8 cm

= 80 square cm

Area of inner rectangle = 4 cm x 6 cm

= 24 square cm

Total area of shaded part = 80 sq. cm – 24 sq. cm

= 56 square cm

Assessment

Find the area of the irregular shapes

Exercise:

Find the area of the shapes shown below.

1.

2.

3.

4.

5.

What we have learned:

• The area of a surface or a plane figure is the number of square units needed to cover the surface or the figure
• Area of the square =  S x S
• Area of the rectangle  =  Length x Width
• Area is measured using standard units
• To find area of irregular shape
• Break the larger area into smaller parts.
• Look for the possibilities in which smaller shapes are part of the larger shape.
• Divide the larger area into smaller rectangles and find the area.

Let Summarize:

To find the area of irregular shapes, the first thing to do is to divid 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 up.