Area of Irregular Shapes

In geometry, we often deal with shapes that can be easily defined such as squares, rectangles, circles and triangles. These are called regular shapes because their sides and angles are predictable. However, in real life, not everything comes in such a neat packaging. This is where irregular shapes come in. An irregular shape is a shape whose sides or angles are not equal. They can be found in many places - in maps, articles, pictures and more. Learning to find the area of these irregular shapes is an important skill.

What is the area?

Area is the space covered by a shape. It is measured in square units such as square centimeters (cm²), square meters (m²), or square inches (in²). To find the area of any regular shape, we use specific formulas. For example:

Square: Area = side x side
Rectangle: Area = Length x Width
Triangle: Area = (base x height) / 2

Understanding irregular shapes

Irregular shapes are not as straightforward. There is no specific formula for their area because their sides are not equal or their angles are not predictable. So, how do we find the area of irregular shapes? The key is to break them down into smaller, regular shapes, whose area we can find using our known formulas.

Area of A = Length of A x Breadth of A = (150 - 50) x (100 - 50) = 100 x 50 = 5000 square units
Area of B = Length of B x Breadth of B = (100 - 50) x (150 - 100) = 50 x 50 = 2500 square units
Total area = Area of A + Area of B = 5000 + 2500 = 7500 square units
    

Steps to find the area of irregular shapes

To find the area of an irregular shape, follow these steps:

• Step 1: Identify the regular shapes into which the irregular shapes can be divided (e.g. rectangles, triangles, etc.).
• Step 2: Measure the required dimensions (such as sides and height) of these regular shapes.
• Step 3: Calculate the area of each regular shape using its specific formula.
• Step 4: Add the areas of all the regular shapes to get the total area of the irregular shape.

Area of rectangle A = (180 - 30) x (100 - 30) = 150 x 70 = 10500 square units
Area of rectangle B = (100 - 30) x (180 - 100) = 70 x 80 = 5600 square units
Total area = Area of A + Area of B = 10500 + 5600 = 16100 square units
    

Real-life applications

Understanding how to find the area of irregular shapes is very useful in everyday life. It can be applied to:

• Gardening or landscaping: When you’re deciding how much grass seed or fertilizer you need for an oddly shaped plot.
• Construction: For calculating flooring materials in a specific size room.
• Arts & Crafts Projects: Ensuring there is enough material to cover surfaces in projects.

Area of trapezium = ((base 1 + base 2) / 2) x height
                  = ((380 + 300) / 2) x (160 - 10)
                  = (680 / 2) x 150 = 340 x 150 = 51000 square units

Area of garden plot = length x breadth = 80 x 60 = 4800 sq. units

Area for grass = Area of trapezoid - Area of garden plot
               = 51000 - 4800 = 46200 square units
    

Useful tips

• Measure carefully: Make sure your measurements are accurate to get the best results.
• Simplify shapes: Try breaking down complex shapes into simpler shapes like rectangles and triangles for easier calculations.
• Use graph paper: If drawing helps, use graph paper; the grid can help visualize and divide shapes into regular pieces.
• Verify results: Always review your parts to ensure there are no missed or duplicated spots due to breakdowns.

Area of part X = Divide it into triangle and rectangle or just based on its identifiable shape.
Suppose it forms a triangle, Area of triangle = (base x height) / 2

Area of part Y (as separately identified or shaped) = length x width

Total area = Area of part X + Area of part Y
    

By practicing these methods, students can become proficient at managing and calculating the areas of irregular bodies, increasing their understanding of places in the world around them.

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