The assessment for this lesson is to participate in a discussion about composite figures. You will be able to participate in the discussion throughout the unit.
You are required to complete the following:
1) Respond to the discussion topic.
2) Respond to your two of your classmates’ ideas as well.
Discussion Topic: What is an example of a composite figure in your home or community? How would you decompose it to find the area? Can you think of another reason that it would be helpful to decompose these figures in addition to making it easier to find the area of the figure?
It needs to be at least two diffrent shapes
An example of a composite figure in my home is a rug. The rug is composed of two shapes, a rectangle and a circle. To find the area of the rug, I would decompose it into the two shapes and calculate the area of each shape separately. Another reason it would be helpful to decompose these figures is to find the perimeter. By decomposing the figure into its individual shapes, it is easier to calculate the perimeter of the figure by adding up the perimeters of the individual shapes.
To find an example of a composite figure in your home or community, look for objects or structures that are made up of two or more distinct shapes. For instance, you might consider a tabletop that consists of a rectangular shape combined with a circular shape for the surface area.
To decompose such a composite figure and find the area, follow these steps:
1) Identify the distinct shapes that make up the composite figure. In our example, these would be the rectangular and circular shapes.
2) Measure the dimensions of each individual shape, which include the length and width of the rectangle and the radius or diameter of the circle.
3) Using the formulas for the areas of the respective shapes (area of rectangle = length x width, area of circle = π x radius^2 or π x (diameter/2)^2), calculate the individual areas of each shape.
4) Sum up the calculated areas of the individual shapes to find the total area of the composite figure.
In addition to making it easier to find the area of a composite figure, decomposing these figures is also helpful for various reasons. One such reason is that it allows you to analyze and understand the different components that make up the figure. Decomposition helps in visualizing how different shapes fit together, providing insights into the structure and design of the figure. It can also aid in problem-solving scenarios where you need to make modifications or adjustments to sections of the composite figure.
Remember, when responding to your classmates' ideas, provide constructive feedback or additional insights to enhance the discussion.
1) Example of a composite figure in my home: One example of a composite figure in my home is a kitchen countertop. It is made up of multiple shapes, such as rectangles and squares, combined together. To decompose it, I would identify each individual shape that makes up the countertop, like rectangular sections and smaller square sections. I would then calculate the area of each of these shapes individually using their respective formulas, and finally add them together to find the total area of the composite figure.
Additionally, decomposing composite figures can be helpful for other reasons apart from finding the area. One reason is that it allows us to understand the structure and configuration of the figure in a better way. By decomposing the figure, we can analyze and visualize how different shapes are arranged together, which can be useful for design and construction purposes.
2) Response to classmate 1: I agree with your example of a composite figure being an outdoor patio. It often comprises both rectangular and circular sections. Decomposing the patio into these shapes and finding their individual areas can be helpful when planning for landscaping or determining the amount of materials needed for construction.
3) Response to classmate 2: I like your example of a composite figure being a bookshelf in a library. It usually consists of various rectangular sections for holding books and smaller square sections for arranging objects like stationary. By decomposing the bookshelf and finding the area of each section, we can determine the capacity of the shelf for holding books and organize them accordingly.