How do we calculate the area of complex shapes?

When students hear the words "compound shapes", they usually feel uncomfortable. Just before you also ask yourself: "Oh, why this again?", you should know that there really is no reason. Describing shapes as compound doesn't really make them so. As it turns out calculating areas and perimeters of compound shapes can actually be relatively straightforward.

You will be introduced to Complex shapes only after you learn various shapes in geometry. The reason these shapes are complex is due to the fact that they are slightly different from those you've come to know. In each complex shape, additional shapes that you need to identify are hidden. Dividing the complex shape into several different (and familiar) shapes will allow you to answer the question of how to calculate the area of complex shapes.

So how do we answer the question of how to calculate the area of complex shapes? First, you need to identify familiar shapes within the complex shape. For example: a rectangle. As you know, each shape has properties that you are familiar with, so within the complex shape itself, you can apply the properties of the familiar shape and thus calculate areas and perimeters.

After completing the missing data (according to the properties of each shape, for example: rectangle), you can complete the "puzzle", identify additional data that becomes apparent, and thus calculate the area of the compound shape. When calculating the area of compound shapes, you will often need to perform simple arithmetic operations like division and addition (especially for sides in the shape) - all based on the unique properties of each shape.

For example: Assuming the composite shape includes several different rectangles, based on the given side lengths, it will be possible to calculate the different areas. The area of a rectangle is calculated using the formula length X width. When the side lengths are visible, subtraction and addition can be performed (according to the sizes of the rectangles and their positions within the shape) of sides, and thus calculate the area of the shape, as seen in the example below.

To calculate the shape's area - we will divide it in a way that creates two rectangles. We will find the area by adding and/or subtracting rectangles.

In this division we created:

A rectangle with size $9 \cdot2 = 18$ rectangle $A$

A rectangle with size $​​​​8 \cdot 6 = 48$ rectangle $B$

The area of the entire composite shape is:

$9\cdot2+8\cdot6=66$

or

$48 + 18= 66$