How do the area and extent differ?
Rectangles and squares: calculate perimeter and area
Extent of rectangles
A second quantity that can be calculated for figures is the circumference. In the case of rectangles and squares, this is also very easy. You just add up all the edge lengths together. The following size can be calculated for the rectangle shown above:
$ U (= circumference) = 8cm + 4cm + 8cm + 4cm $
The circumference $ U $ of a rectangle results from the addition of the side lengths:
$ U = 2 \ cdot (a + b) $
Area and perimeter for squares
These calculations work the same way with squares, except that all lengths are equal.
The area $ A $ of a square is also calculated from the product of the side lengths:
$ A = a \ cdot a = a ^ 2 $
The following applies to the circumference $ U $ of a square: $ U = 4 \ cdot a $
The simple calculations for area and circumference for rectangles will be used again and again in the following examples. In the case of more complicated shapes, the procedure is usually to break the figure down into rectangles in order to get a result as easily as possible.
Calculate rectangle: example
Now let's do an example calculation. First try to determine the solution yourself and then take a look at it here.
Now calculate the circumference (U) and the area (A) of a rectangle. The side lengths are $ a = 6 cm $ and $ b = 3 cm $
Let's start by calculating the perimeter of our rectangle. According to the formula that you have already got to know, you calculate the circumference with: $ 2 \ cdot (a + b) $. Let's insert our values for a (6 cm) and b (3 cm) into this formula and you get $ U = 2 \ cdot (6cm + 3cm) $. If we do the math, we get $ 2 \ cdot 9cm $, which is $ 18cm $. The circumference is $ U = 18 cm $.
Next we want to deal with the calculation of the area. We take the well-known formula (A = a $ \ cdot $ b) and insert our values here as well: $ A = 6cm \ cdot 3cm $. You get the area $ A = 18 cm ^ 2 $. Did you come up with the same solutions?
Test and deepen your new knowledge in the exercises! Good luck with it!
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