Decomposing a figure means breaking it down into smaller shapes that we already know how to find the area of, and then adding up their areas to find the total area of the original figure. This can be really helpful when we have a complicated shape that we don't know how to find the area of directly.
Let's take an example of a rectangle with a triangular piece cut out of it. If we try to find the area of this shape directly, it can be a little tricky. But if we decompose the figure into a rectangle and a triangle, we can find the area of each shape and add them up to find the total area of the figure.
First, we find the area of the rectangle by multiplying its length and width. Let's say the length is 10 units and the width is 6 units. The area of the rectangle is 10 x 6 = 60 square units.
Next, we find the area of the triangular piece that was cut out. The formula for the area of a triangle is (base x height) / 2. Let's say the base of the triangle is 6 units and the height is 4 units. The area of the triangle is (6 x 4) / 2 = 12 square units.
Now we just add the areas of the rectangle and the triangle to find the total area of the original figure.
Total area = Area of rectangle + Area of triangle Total area = 60 square units + 12 square units Total area = 72 square units
So the total area of the figure is 72 square units.
Decomposing a figure can make finding its area much easier. It's like taking apart a puzzle and putting it back together, but with shapes instead of puzzle pieces!