Composite shapes are figures made up of two or more simple geometric shapes. To find the area of a composite shape, you need to break it down into simpler shapes, calculate the area of each, and then combine those areas.
Steps to Find the Area of Composite Shapes
1. Identify the Simple Shapes
First, look at the composite shape and identify the simple geometric shapes that make it up. These could be rectangles, triangles, circles, or other polygons.
2. Calculate the Area of Each Simple Shape
Use the appropriate formula for each simple shape:
- Rectangle: $A = l times w$, where $l$ is the length and $w$ is the width.
- Triangle: $A = frac{1}{2} times b times h$, where $b$ is the base and $h$ is the height.
- Circle: $A = pi r^2$, where $r$ is the radius.
- Trapezoid: $A = frac{1}{2} (a + b) h$, where $a$ and $b$ are the lengths of the parallel sides and $h$ is the height.
3. Add or Subtract the Areas
Once you have the areas of the individual shapes, add them together if they are all part of the composite shape. If any part of the shape is subtracted (like a hole), subtract that area from the total.
Example
Let’s find the area of a composite shape consisting of a rectangle and a semicircle.
- Identify the Shapes
- Rectangle: Length = 8 cm, Width = 4 cm
- Semicircle: Radius = 2 cm
- Calculate the Areas
- Rectangle: $A_{rectangle} = 8 times 4 = 32 text{ cm}^2$
- Circle: $A_{circle} = pi times 2^2 = 4pi approx 12.57 text{ cm}^2$
- Semicircle: $A_{semicircle} = frac{1}{2} times 12.57 approx 6.28 text{ cm}^2$
- Add the Areas
- Total Area: $A_{total} = 32 + 6.28 approx 38.28 text{ cm}^2$
Conclusion
Finding the area of composite shapes involves breaking the shape down into simpler components, calculating the area of each, and then combining those areas. This method can be applied to a variety of composite shapes, making it a versatile and useful skill in geometry.
3. BBC Bitesize – Composite Shapes