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. In the example below, the shape can be seen as a rectangle with a triangle cut out. Finding the dimensions Example: Subtracting one area from another When tutoring your children, give help, when needed, to find these “missing” dimensions. The example above illustrates a common requirement when working with compound shapes – finding dimensions that are not shown. The shape can be seen as a triangle combined with a rectangle. The area calculation example below is relatively simple. 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. 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. 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 πr 2 Circle Sectors Rearranged Circle Sectors Rearranged – Starting to Look Like a Rectangle Area of Compound Shapes Note: There is no limit to how small these sectors could be and to how closely they could resemble a rectangle when arranged.Īssuming we know that the circumference of a circle is equal to 2πr we can add dimensions to the “rectangle” as shown below. Notice how, as the sectors become smaller, the shape becomes more like a rectangle. Take a circle and divide it into equally sized sectors and rearrange these as shown below. You can find out more about Pi here Example of calculating the area of a circle Explanation of the Area of a Circle Formula Π (pronounced “pie” and often written “Pi”) is an infinite decimal with a common approximation of 3.14159. Where r is the radius of the circle and π is the ratio of a circle’s circumference to its diameter. The length and width of a square are the same so we just need to multiply the length by the length. More Examples of Calculating Area Area of a Square 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. 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. The only problem with this is that we would end up having to use very big numbers. We could use small squares to measure large areas. We can say “63 millimeters squared” or ” 63 square millimeters” We write square sizes using a small 2 next to the unit. We use different sizes of squares depending on how big or small an area is. The area of a rectangle is = length x widthĮxamples of calculating the area of a rectangle Units for measuring area The rectangle above has an area of 15 square units. We can count the squares or we can take the length and width and use multiplication. Calculating AreaĪrea is measured in squares (or square units). Knowing the area of the room will help make sure that the carpet you buy is big enough without having too much left over. Think of getting a new carpet fitted in a room in your home. 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.
It tells us the size of squares, rectangles, circles, triangles, other polygons, or any enclosed figure.
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