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What is area?
Area tells us the size of a shape or figure. It tells us the size of squares, rectangles, circles, triangles, other polygons, or any enclosed figure.
In the real world it tells us the size of pieces of paper, computer screens, rooms in houses, baseball fields, towns, cities, countries, and so on. Knowing the area can be very important. Think of getting a new carpet fitted in a room in your home. Knowing the area of the room will help make sure that the carpet you buy is big enough without having too much left over.
Calculating Area
Area is measured in squares (or square units).
How many squares are in this rectangle?
We can count the squares or we can take the length and width and use multiplication. The rectangle above has an area of 15 square units.
The area of a rectangle is = length x width
Examples of calculating the area of a rectangle
Units for measuring area
We measure area using squares. We use different sizes of squares depending on how big or small an area is.
We could use small squares to measure large areas. The only problem with this is that we would end up having to use very big numbers. For example, a field might be measured at 5,000,000,000 square millimeters when 5,000 square meters would be a much easier size to say, write, and visualize.
You will probably hear more units for measuring area; square inches, square feet, square yards, square miles, acres, hectares are all units used for measuring area.
More Examples of Calculating Area
Area of a Square
The length and width of a square are the same so we just need to multiply the length by the length.
Area of a Circle
The area of a circle = πr2
where r is the radius of the circle and π is the ratio of a circle's circumference to its diameter.
π (pronounced 'pie' and often written 'Pi') is an infinite decimal with a common approximation of 3.14159. You can find out more about Pi here
Example of calculating the area of a circle
Explanation of the Area of a Circle Formula
Take a circle and divide it into equally sized sectors and rearrange these as shown below. Notice how, as the sectors become smaller, the shape becomes more like a rectangle. Note: There is no limit to how small these sectors could be and to how closely they could resemble a rectangle when arranged.
Assuming we know that the circumference of a circle is equal to 2πr we can add dimensions to the 'rectangle' as shown below. Using the area of a rectangle area formula, area = width x height we can see how our circle, re-configured as a rectangle, can be shown to have an area that approximates to πr x r or πr2
Circle Sectors Rearranged
Circle Sectors Rearranged - Starting to Look Like a Rectangle
Cut Out Shapes 8 3 15 2 X
Area of Compound Shapes
There are many cases where the calculation of a total area requires more than one area to be calculated followed by either an addition, subtraction, or some other combination of operations to find the required area.
Note: In the examples below the units of measurement are not shown and answers and the value of π (Pi) have been rounded to the nearest hundredth. Privatus 5 0 1 – automated privacy protection.
Example: Simple Compound Shapes
The area calculation example below is relatively simple. The shape can be seen as a triangle combined with a rectangle.
The example above illustrates a common requirement when working with compound shapes - finding dimensions that are not shown. When tutoring your children, give help, when needed, to find these 'missing' dimensions. There is another example below.
Finding the dimensions
Example: Subtracting one area from another
In the example below, the shape can be seen as a rectangle with a triangle cut out.
Example: Partial areas
The example below is similar to one above although, since we have a semi-circle we need to calculate a fraction (one-half) of the circle's area. Note in this example the diameter, and not the radius is shown.
Example: Decisions! Combine? Subtract
It is common to have more than one way to calculate the final area. In the examples below the shape can be seen as two rectangles combined or as one large rectangle with a smaller rectangle 'cut out' from the top right corner.
Calculating Area Worksheets
Print out the worksheets listed below and use them for practice when tutoring your children.
- Calculating Compound Areas e.g. with rectangular shapes
- Calculating Compound Areas e.g. with rectangles, triangles, and circles
- Calculating Areas e.g. of Triangles
- Calculating Surface Areas e.g. of Rectangular Prisms
You will find more printable geometry worksheets here.
One Geometry topic that is introduced at a young age and then explored in more complex ways as kids get older is 3D shapes. Obviously, the first thing young mathematicians learn is to simply recognize the shapes, learn their names and discover them in the world around us. As kids get older, it's important to help them learn and understand polyhedron nets. Understanding what these shapes look like 'flat' helps with spatial sense and reasoning and will build a solid foundation for later study of surface area. These simple 3D shapes worksheets can help students make connections and understand 3D shapes and their nets!
Below are a few introductory worksheets on the topic of three dimensional shapes. These can be used in upper elementary or middle school, depending on the level of your students, or as a quick review in a high school Geometry class. I hope you find them helpful!
Included in this download are 3 different practice worksheets. The first is a chart to help students learn the properties of various 3D shapes, as well as compare them and find real life examples.
The second worksheet is a simple matching page to help kids determine the nets (what each shape looks like taken apart and laid flat) of each of the 3D shapes.
The third worksheet is a little more challenging. This page gives various images, and students have to determine whether or not they are the nets of actual polyhedron. This requires the use of spatial reasoning skills and can help them recognize actual nets.
If your kids are having trouble determining the figures, encourage them to cut out a piece of paper and see if they can fold it into a shape, rather than guessing or giving up.
{Click HERE to go to my shop and get the 3D shapes worksheets!}
Would you like to have an easy to use set of printable and foldable nets for further polyhedron exploration? Check out these free downloadable nets pages!
Need more 3D Shape resources? Try one of the following:
Enjoy!
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