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How can I find the area of a rectangular figure by breaking it apart?
Goal:
Goal:
Think About It!
Goal: Deconstruct a rectangle to find its area.
Logan has been doing some research. He found that paper airplanes come in all different styles and shapes, but they all start with rectilinear shapes, or shapes made of right angles.
Many airplanes of different sizes, shapes, and folding styles, flying through the air.
Area is the number of unit squares needed to cover a flat surface. It is the entire amount of space inside a space or figure, like the size of a panel. Remember that area is always measured in square units.
Click on the steps below to see how to use addition to help find the area of rectangular shapes.
Remember, when you have a shape like the one below that has different areas of rectangular shapes, you must decompose, or break, the shape into smaller shapes.
A rectangle that looks like two rectangles combined, however one is smaller than the other. The entire rectangle is 8 inches in length. The first part of the rectangle is 5 inches wide. The second part is 2 inches wide and 3 inches in length. to decompose the rectangle you can seperate the shape vertically up and down at 3 inches and lenght and it will give you two seperate rectangles.
If we look at the example above, this shape can be separated into two separate rectangular shapes.
Let’s see how to find the measurements of each part!
If we know that the length of the smaller section is 3 inches and the total measure of the opposite side is 8 inches, we can determine that the length of the larger section is 5 inches: \({8 - 3 = 5}\).
A rectangle that looks like two rectangles combined, however one is smaller than the other. The entire rectangle is labelled 8 inches in length. The first part of the rectangle is 5 inches wide and is labelled 5 inches in length. The second part is 2 inches wide and is labelled 3 inches in length. to decompose the rectangle you can seperate the shape vertically up and down at 3 inches and lenght and it will give you two seperate rectangles.
Find the area of each shape.
A rectangle that looks like two rectangles combined, however one is smaller than the other. The first part of the rectangle is 5 inches wide and is labelled 5 inches in length. The second part is 2 inches wide and is labelled 3 inches in length. to decompose the rectangle you can seperate the shape vertically up and down at 3 inches and lenght and it will give you two seperate rectangles.
The area of the larger shape is 5 in by 5 in.
Area = 5 in x 5 in = 25 in\({^2}\)
Do you notice “in\({^2}\)” after the 25? This is another way to write square inch! The “in” stands for inch, and the 2 tells us it is squared. You can write many measurements this way: ft\({^2}\), cm\({^2}\), unit\({^2}\), etc. It is just a shorter way to label it than writing out square inches!
The area of the smaller shape is 2 in by 3 in
Area \({=}\) 2 in \({\times}\) 3 in \({=}\) 6 in\({^2}\)
Combine what you know to find the total area.
A rectangle that looks like two rectangles combined, however one is smaller than the other. The first part of the rectangle is 5 inches wide and is labelled 5 inches in length. The second part is 2 inches wide and is labelled 3 inches in length. to decompose the rectangle you can seperate the shape vertically up and down at 3 inches and lenght and it will give you two seperate rectangles. To find the total area we can use the following equations 5 in \({\times}\) 5 in \({=}\) 25 in\({^2}\) 2 in \({\times}\) 3 in \({=}\) 6 in\({^2}\) 25 in\({^2}\) \({+}\) 6 in\({^2}\) \({=}\) 31 in\({^2}\)
Area of the large shape \({+}\) Area of small shape \({=}\) Total Area 25 in\({^2}\) + 6 in\({^2}\) = 31 in\({^2}\)!
Let’s see if we can help Logan break apart rectangular figures and calculate the total area using other pieces of paper.