Math resources Geometry Area

Area of Irregular Shapes

Area of irregular shapes

Here you will learn about the area of irregular shapes, including what irregular shapes are, and questions involving rectilinear shapes, missing side lengths and unit conversion.

Students will first learn about finding the area of an irregular shape as part of geometry in 3 rd grade. Students will deepen their understanding of area of irregular shapes in 4 th grade.

What is the area of irregular shapes?

The area of irregular shapes (also referred to as irregular polygons or irregular figures) is the amount of space inside a shape composed of sides and angles of different lengths and sizes.

It is measured in square units (\mathrm{cm}^{2},\mathrm{~m}^{2},\mathrm{~mm}^{2} etc.).

To find the area of irregular shapes, you will decompose the irregular shape into regular shapes, such as triangles or regular polygons, then find the area of each of the regular shapes and add them together.

Some of the common regular shapes used when decomposing irregular shapes are rectangles, squares, triangles, circles or semicircles, and trapezoids.

For example,

This irregular shape was split into two shapes, a rectangle (shape A ) and a square (shape B ). Find the area of the rectangle and the area of the square, and then add the two areas together.

Area of irregular shapes 1 US

[FREE] Area Check for Understanding Quiz (Grade 4 to 6)

[FREE] Area Check for Understanding Quiz (Grade 4 to 6)

[FREE] Area Check for Understanding Quiz (Grade 4 to 6)

Use this quiz to check your grade 4 to 6 students’ understanding of area. 15+ questions with answers covering a range of 4th, 6th and 7th grade area topics to identify areas of strength and support!

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[FREE] Area Check for Understanding Quiz (Grade 4 to 6)

[FREE] Area Check for Understanding Quiz (Grade 4 to 6)

[FREE] Area Check for Understanding Quiz (Grade 4 to 6)

Use this quiz to check your grade 4 to 6 students’ understanding of area. 15+ questions with answers covering a range of 4th, 6th and 7th grade area topics to identify areas of strength and support!

DOWNLOAD FREE

Area of irregular shapes using a square grid

Sometimes when finding the area of irregular shapes, they will be presented to you on a square grid. You can find the area of shapes using the square grid by simply counting the squares.

For example, to find the area of the given shape below, you can just count the number of squares, or space, the shape takes up.

Area of irregular shapes 2 US

The area of this irregular shape is 7 square units.

What is the area of irregular shapes?

What is the area of irregular shapes?

Common Core State Standards

How does this relate to 3 rd grade math and 4 th grade math?

  • Grade 3 – Measurement and Data (3.MD.7, 3.MD.7.d)
    Relate area to the operations of multiplication and addition; Recognize area as additive. Find areas of rectilinear figures by decomposing them into non-overlapping rectangles and adding the areas of the non-overlapping parts, applying this technique to solve real world problems.

  • Grade 4 – Measurement and Data (4.MD.3)
    Apply the area and perimeter formulas for rectangles in real world and mathematical problems. For example, find the width of a rectangular room given the area of the flooring and the length, by viewing the area formula as a multiplication equation with an unknown factor.

How to find the area of irregular shapes

In order to find the area of irregular shapes:

  1. Break down the irregular shape into regular shapes.
  2. Find the area of each basic shape.
  3. Add the areas.
  4. Write down your final answer with square units.

Area of irregular shapes examples

Example 1: using a square grid

Find the area of the given irregular shape.

Area of irregular shapes 3 US

  1. Break down the irregular shape into regular shapes.

This shape can be broken down into 2 rectangles.

Area of irregular shapes 4 US

2Find the area of each basic shape.

Find the area of each shape by counting the square units present.

Area of irregular shapes 5 US

3Add the areas.

\text{Area}=A+B=28+32=60

4Write down your final answer with square units.

60 square units.

Example 2: using a square grid

Find the area of the given irregular shape.

Area of irregular shapes 6 US

Break down the irregular shape into regular shapes.

Find the area of each basic shape.

Add the areas.

Write down your final answer with square units.

Example 3: word problem

Bridges High School is putting in a flower bed in the courtyard. The sketch below shows the flower bed in square feet. What is the area of the new flower bed?

Area of irregular shapes 9 US

Break down the irregular shape into regular shapes.

Find the area of each basic shape.

Add the areas.

Write down your final answer with square units.

Example 4: irregular shapes (all sides given)

Find the area of the irregular shape below.

Area of irregular shapes 12 US

Break down the irregular shape into regular shapes.

Find the area of each basic shape.

Add the areas.

Write down your final answer with square units.

Example 5: irregular shapes (missing sides)

Find the area of the irregular shape below.

Area of irregular shapes 15 US

Break down the irregular shape into regular shapes.

Find the area of the basic shapes.

Add the areas.

Write down your final answer with square units.

Example 6: word problem

Emma built a dog run that has two dog lanes and space in the middle for a water area. She divided the dog run as seen below. The shape has a horizontal and vertical line of symmetry. What is the total area of her new dog run?

Area of irregular shapes 21 US

Break down the irregular shape into regular shapes.

Find the area of the basic shapes.

Add the areas.

Write down your final answer with square units.

Teaching tips for area of irregular shapes

  • While area of irregular shapes worksheets are necessary to allow for student practice, providing students with visual aids, such as grid paper and colored shapes, can help students visualize the decomposition of irregular shapes into regular shapes.

  • When creating lesson plans, make sure to incorporate the many different technology tools that exist that can help students find the area of irregular shapes.

  • Have students work collaboratively to create study materials, such as a step-by-step guide or examples that have been solved. These can assist students by giving them something to study outside of the classroom, and refer back to as often as needed.

Easy mistakes to make

  • Miscounting squares when using a square grid
    Take care when counting squares using a square grid. Find a way to mark each square so you don’t end up counting the same square more than once, or forgetting a square all together. It’s also important to note any partial squares that can be added as fractions.

  • Using the wrong formulas when calculating area
    Label each type of basic or regular shape based on its properties. It’s important to be familiar with how to find the area of each of these shapes, including the area of the triangle.

  • Forgetting to add up all individual shapes
    Labeling each individual shape with a letter or number can help ensure that you do not forget a shape when calculating the total area.

    Writing an equation with each of the shapes ( for example, \text{Area}=A+B+C) before starting any math calculations can help make sure you account for each area.

Practice area of irregular shapes questions

1. Find the area of the irregular shape.

 

Area of irregular shapes 25 US

28 square units

GCSE Quiz False

48 square units

GCSE Quiz True

20 square units

GCSE Quiz False

52 square units

GCSE Quiz False

Split the irregular shape into smaller, regular shapes, and then count the squares within the shape to find the area.

 

Area of irregular shapes 26 US

 

8+12+28=48 square units

2. Find the area of the irregular shape.

 

Area of irregular shapes 27 US

144 square units

GCSE Quiz False

48 square units

GCSE Quiz False

80 square units

GCSE Quiz False

96 square units

GCSE Quiz True

Split the irregular shape into smaller, regular shapes, and then count the squares within the shape to find the area.

 

Area of irregular shapes 28 US

 

32+16+48=96 square units

3. Find the area of the irregular shape.

 

Area of irregular shapes 29 US

40 square meters

GCSE Quiz False

77 square meters

GCSE Quiz False

45 square meters

GCSE Quiz False

85 square meters

GCSE Quiz True

Divide the shape into 2 rectangles, and find the area of each rectangle.

 

Area of irregular shapes 30 US

 

A=3\times{15}=45

 

B=5\times{8}=40

 

\text{Area}=45+40=85\mathrm{~m}^2

4. The irregular shape below has one horizontal line of symmetry.

 

Find the area of the irregular shape.

 

Area of irregular shapes 31 US

96\mathrm{~cm}^2
GCSE Quiz False

12\mathrm{~cm}^2
GCSE Quiz False

94.5\mathrm{~cm}^2
GCSE Quiz True

87\mathrm{~cm}^2
GCSE Quiz False

Divide the shape into a rectangle and a triangle, then use the appropriate formulas to find the area of both shapes.

 

Area of irregular shapes 32 US

 

A=7\times{12}=84

 

B=(3\times{7})\div{2}=10.5

 

84+10.5=94.5\mathrm{~cm}^2

5. Kimberly is replacing the flooring in 3 of the rooms in her house and the hallway between them. The plan of the rooms has a horizontal and vertical line of symmetry.

 

Area of irregular shapes 33 US

 

What is the total area of flooring that Kimberly will replace?

117\mathrm{~ft}^2
GCSE Quiz False

54\mathrm{~ft}^2
GCSE Quiz False

213\mathrm{~ft}^2
GCSE Quiz False

288\mathrm{~ft}^2
GCSE Quiz True

Divide the areas into 3 rectangles and find the area of each. As the shape has two lines of symmetry, write the missing side lengths, including any calculated length.

 

(13-9)\div{2}=2\mathrm{~ft}

 

Area of irregular shapes 34 US

 

A=13\times{9}=117

 

B=9\times{6}=54

 

C=13\times{9}=117

 

\text{Area}=117+54+117=288\mathrm{~ft}^2

6. A city park has an irregular shape that is divided into three sections: a rectangular playground, a triangular garden and a square picnic area.

 

Area of irregular shapes 35 US

 

What is the total area of the city park?

330\mathrm{~ft}^2
GCSE Quiz False

571\mathrm{~ft}^2
GCSE Quiz True

196\mathrm{~ft}^2
GCSE Quiz False

45\mathrm{~ft}^2
GCSE Quiz False

Find the area of the three regular shaped areas to find the total area of the irregular shape.

 

Playground:

 

\text{Area}=l\times{w}=22\times{15}=330

 

Picnic Area:

 

\text{Area}=l\times{l}=14\times{14}=196

 

Garden:

 

\text{Area}=\cfrac{1}{2}\times{b}\times{h}=\cfrac{1}{2}\times{6}\times{15}=45

 

\begin{aligned}\text{Total area}&=\text{Playground}+\text{Picnic area}+\text{Garden} \\\\ &=330+196+45 \\\\ &=571\mathrm{~ft}^2 \end{aligned}

Area of irregular shapes FAQs

What is an irregular shape?

An irregular shape is any shape that does not have equal sides or angles. These shapes cannot be classified by any standard geometric names, like squares or triangles. Some examples of irregular shapes include polygons with different side lengths and shapes with curved boundaries.

How do you find the area of composite figures?

You can find the area of composite figures, or shapes, similarly to how you find the area of irregular shapes. You can break the composite shape into basic shapes, find the area of each individual shape, and then add the sums together to find the total area of the composite shape.

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