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Learn how to split tricky shapes into rectangles, find each area, and add them up!
People have needed to measure the size of flat surfaces for thousands of years. Farmers wanted to know how big their fields were. Builders needed to know how much stone to cut for a floor. Even kids sharing a pizza want to know who got the bigger piece! The idea of area — how much space a flat shape covers — has been important for a very long time.
Here is the big question we will answer: What do you do when a shape is NOT a simple rectangle? You break it into pieces that ARE rectangles, find each area, and add them together. Let's learn how!
Before we start splitting shapes, let's make sure we know four important ideas. Read each card below carefully.
Look at the L-shaped figure below. It is a rectilinear shape because every corner is a right angle. We draw one line to split it into Rectangle A and Rectangle B. Then we find each area and add.
See the dashed yellow line? It splits the L-shape into two rectangles that do not overlap. Rectangle A is 7 cm wide and 3 cm tall. Rectangle B is 8 cm wide and 4 cm tall. To find the total area, we find each area and add them together.
Here are the three steps you will use every time you see a rectilinear shape. Follow these and you'll always get the right answer!
You can sometimes split the same shape in different ways. That's okay! No matter how you split it, the total area will be the same. That is what "area is additive" means.
Not every rectilinear shape is an L. Some look like a T, a U, or even a plus sign (+). The good news is: the same trick works every time. Let's look at a T-shape.
The T-shape above has two parts. Rectangle C (the top bar) is 10 cm × 2 cm = 20 cm². Rectangle D (the stem) is 2 cm × 5 cm = 10 cm². The total area is 20 + 10 = 30 cm².
Here is a handy table showing common rectilinear shapes and how many rectangles you might need.
| Shape | Looks Like | Rectangles Needed |
|---|---|---|
| L-shape | A book with a piece cut off | 2 |
| T-shape | A letter T or a hammer | 2 |
| U-shape | A horseshoe or goal post | 3 |
| Plus sign (+) | A first-aid cross | 3 (or 2 with overlap thinking) |
| Staircase | Steps going up | 2, 3, or more |
Let's solve a full problem together. Read each step slowly.
You've now seen two ways to find the area of a rectilinear shape. Both work! Here's a quick comparison so you know when each method is handy.
| Splitting (Decomposing) | Subtracting | |
|---|---|---|
| What You Do | Draw lines to break the shape into rectangles. Find each area and add. | Picture a big rectangle around the whole shape. Find its area, then subtract the missing part. |
| Best For | L-shapes and T-shapes where the split is easy to see. | U-shapes and shapes with a notch cut out of one side. |
| Number of Calculations | 2 or 3 multiplications, then add. | 2 multiplications, then subtract. |
| Common Mistake | Accidentally overlapping two rectangles (counting some area twice). | Forgetting to subtract, so the area is too big. |
Right now you are working with shapes that have only right angles (rectilinear shapes). As you move through math, you'll start finding the area of triangles, trapezoids, and even circles. The big idea stays the same: you can almost always break a tricky shape into simpler shapes you already know how to measure.
| What You Learn Now | What You'll Learn Later | |
|---|---|---|
| Shapes | Rectangles and rectilinear figures | Triangles, parallelograms, circles |
| Strategy | Split into rectangles, add areas | Split into triangles and rectangles, use new formulas |
| Core Idea | Area is additive | Area is still additive! (This never changes.) |
So everything you practice today is building a super-strong foundation. The idea that area is additive will be your friend all through school!
Try these five problems on your own. Click "Show Answer" when you're ready to check your work. Good luck!
Area is the amount of flat space inside a shape, measured in square units. A rectilinear shape is a figure made only of straight sides and right-angle corners — like rectangles stuck together to form an L, T, U, or other step-like shape. The big idea is that area is additive: you can decompose (break apart) any rectilinear figure into non-overlapping rectangles, find the area of each rectangle using length × width, and then add all the areas together to get the total.
You can also find the area by picturing a big rectangle around the whole shape and subtracting the missing parts. Both strategies work because area is additive — no matter how you split or subtract, you get the same total. This idea will help you all through math, even when you meet triangles, circles, and other shapes later on!