Area of Composite Figures - Rectangles

Area of a Composite Figure

A composite figure (also known as a compound figure or composite shape) is a two-dimensional geometric figure made up of two or more basic geometric shapes. These basic shapes can include rectangles, squares, triangles, circles, semi-circles, trapezoids, parallelograms, etc.

Calculating the area of a composite figure involves breaking it down into these simpler, familiar shapes, calculating the area of each component, and then combining those areas appropriately.

The following figures show how to find the area of a composite figure. Scroll down the page for more examples and solutions.

 

Geometry Worksheets
Practice your skills with the following worksheets:
Printable & Online Geometry Worksheets

Steps to Calculate the Area of a Composite Figure:

1. Decompose the Figure:
   Divide the complex figure into smaller, non-overlapping basic shapes (like rectangles, triangles, semi-circles).
   Sometimes, you may need to calculate the area of the larger shape and then subtract the area of the “missing” part.
   

2. Identify Missing Dimensions:
   Often, not all side lengths or heights will be directly given. You’ll need to use the given dimensions and the properties of the basic shapes (e.g., opposite sides of a rectangle are equal) to find any necessary missing measurements.
   

3. Calculate the Area of Each Basic Shape:
   Use the standard area formulas for each of the simpler shapes you’ve identified. Make sure you know the formulas for common shapes:
   Rectangle: A = length×width
   Square: A = side²
   Triangle: A = 1/2×base×height
   Circle: A = πr²
   Semi-circle: A = 1/2 πr²
   Trapezoid: A = 1/2 (base1 + base2)×height
   

4. Combine the Areas:
   Sum the areas of all the individual basic shapes. Or subtract the area of the “cut-out” section from the area of the larger shape.

5. State the Final Area with Units:
   Always remember to include the appropriate square units

Videos

Area of Composite Shapes
This shows how to work out the area of composite rectangular shapes.

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Perimeter and Area of Irregular Shapes

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Area of Composite Figures (Rectangles)
Finding Shaded Area of Rectangular Shapes

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