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Math Worksheets For All Ages

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Math Worksheets For All Ages

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Finding the Area of Composite Shapes

Many times, we will come across a familiar shape or figure. They may not be clearly definable geometric shapes such as circles, triangle, or rectangles, but they are mixture of them. We call these figures that are a combination of common geometric shapes composite shapes. There are times when we will need to determine the area of these composite shapes. If you break the overall composite figure into clearly definable unique geometric shapes and find the measures of all those shapes, you can easily determine it. The collective area of all these figures will be the overall area of the composite shape. The lessons and worksheets that we put forth in this section will teach you how to determine these values for yourself.

Aligned Standard: Grade 6 Geometry - 6.G.A.4

    This is a very diverse skill. I included some advanced work in here that includes the use of Pythagorean theorem for advanced students.

  • School Composition Step-by-step Lesson- What is the ratio of boys to girls?
  • Guided Lesson - How much money did Peter go to the store with? How many runs did Rich account for?
  • Guided Lesson Explanation - We test both skills here.
  • Practice Worksheet - Problems #3 and #4 are more advanced skills. If you want more basic skills, see the practice sheets below.
  • Answer Keys - These are for all the unlocked materials above.

Practice Worksheets

Practice sheets 2-5 are perfect aligned to the standards. Sheets 6-9 are for your more advanced students that have a good hold on geometry.

  • Practice Sheet 2 - A park has a beautiful green grass bed in the center. Find the area of its green grass bed
  • Practice Sheet 3 - Find the required measures of the yellow shaded complex shape. All the squares are 1cm by 1cm.
  • Practice Sheet 4 - This will require you to look at many new figures and collections of them.
  • Practice Sheet 5 - Calculate all the measures that you are asked for of the shaded regions.
  • Practice Sheet 6 - A circular shaped garden with a radius of 10m is full of green grass, except a square concrete platform with side lengths of 4m. Find the area of the land covered by grass.
  • Practice Sheet 7 - Find the needed measures of the portion of a basketball court shown in the figure below.
  • Practice Sheet 8 - A 100 m long and 70 m wide rectangular park has an inner walking path that is 5 m wide around the park. What are the required measures of the walking path?
  • Practice Sheet 9 - A circular green grass garden is surrounded by a walking path as shown in the figure. See what you can make of all the values that are put in your direction.


How to Find the Area of Composite Shapes

Calculating the area of geometrical shapes is one of the most significant concepts in mathematics, as it is very frequently used in daily life. From calculating the area of the table for its cover to the sowing the garden, or at the time of purchasing a carpet for a room. It is how we go about purchasing and selling all types of different things. It is also how we begin and plan the construction of dwellings like buildings and additions to buildings.


Calculating the these measures of straightforward shapes such as squares, rectangles, triangles, and circles is very simple. In real life, you will have to deal with a lot of shapes that will not be regular polygons or straightforward shapes. It is due to this reason it is crucial to learn to calculate the area of composite shapes. A composite shape is the one that is made of several geometric shapes such as semi-circles, rectangles, squares, and triangles. Calculating the area for composite shapes might seem a bit complicated, but if you follow these simple steps, you do not have to worry about these area problems.


Step 1: Separate the Shapes - The first step is to divide the shape into the shapes you can identify within it. You can separate them. You need to be careful about the dimensions here.


Step 2: Measures of Separate Shapes - Now that you have separated the different figures with their dimensions, you can calculate the area of all these figures separately.


Step 3: Sum of All Measures - After finding out the area for each figure, you need to sum all these together. The final answer will be the area of the composite figures.


How Does This Skill Relate to The Real World?


Just about any form of construction requires this skill. It does not matter if you are constructing a building from scratch or just changing the carpet in one of your rooms. Carpenters and foremen use this skill almost every single hour. This is because the architecture of most structures is not formed as perfect squares. In order to determine how much material you will need to complete a project that has any other shape then a square, takes some quick thinking and planning. It is best to size up the shapes into definable areas for yourself. Once you have them formed into digestible areas, you can then authenticate the values. In the United States, we are focused on the square footage of the areas we will work on. This will dictate the costs associated with materials and the amount of time a project would take to complete.

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