Area of Irregular Shapes Worksheet (Free, With Answer Key)
Nine practice problems across three methods. Work through them, then check your answers below — and print or save as PDF when you’re done.
Section A: Grid (Graph Paper) Method
Count full squares as 1. Count squares that are at least half-covered as ½. Ignore anything less than half.
A1. Count the squares in this L-shape. Each square = 1 unit².
A2. Count the squares in this T-shape. Each square = 1 unit².
A3. Count the squares in this step shape. Each square = 1 unit².
Section B: Missing Sides Method
Not every side is labeled. Use the sides you know to work out the one you don’t before calculating area.
B1. Find the area. One side is missing — work it out first.
Outer width 10, outer height 8, notch cut from the top-right sized 4 wide by 3 tall.
B2. Outer width 12, outer height 9, notch cut from one corner sized 5 wide by 4 tall. What’s the missing top segment, and the total area?
B3. Outer width 14, outer height 10, notch cut from one corner sized 6 wide by 4 tall. What’s the missing segment, and the total area?
Section C: Decomposition (Rectangle + Triangle)
Split the shape into a rectangle and a triangle, find each area, then add them together.
C1. Find the area of this house-shaped figure.
C2. A rectangle measuring 6 by 4 has a triangle attached to one side, with base 4 and height 4. Find the total area.
C3. A rectangle measuring 10 by 6 has a triangle attached to each end, each with base 3 and height 6. Find the total area.
Every irregular shape worksheet online basically says the same thing: split it into rectangles and triangles, then add. That part’s true, and it’s the right idea. But it skips two things that actually trip students up — what to do when a side isn’t labeled, and how the grid-counting method really works, square by square. This worksheet covers both, with real answers, not just a formula repeated three times.
Method 1: The Grid (Graph Paper) Method
This is the method most students learn first, because it doesn’t need any formula at all — just counting.
Trace the shape onto graph paper, or draw it directly on a grid. Then count squares: a full square counts as 1, a square that’s more than half covered counts as 1, a square that’s roughly half covered counts as ½, and anything less than half doesn’t count at all.
This method gives an estimate, not an exact answer — real curved or oddly-angled shapes won’t line up perfectly with grid lines. But for shapes made of straight, grid-aligned edges (like the three problems in Section A), it gives an exact count every time.
Method 2: The Missing Sides Method
Real worksheets — and real rooms, lots, and floor plans — don’t always label every single side. Section B is built around this exact situation: an L-shaped figure where one side is left blank, and you have to work it out before you can find the area at all.
The trick is simple once you see it: in a rectilinear shape (all right angles), opposite sides that run the same direction have to add up correctly. If the outer width is 10 and a notch cut into it is 4 wide, the remaining top segment has to be exactly 6 — there’s no other option, because 4 plus 6 makes the full 10 again.
Once every side is accounted for, the area itself works the same way as any other decomposition problem: split the shape, calculate each piece, add them up — or, for a notched rectangle, calculate the full outer rectangle and subtract the notch.
Method 3: Decomposition (Rectangle + Triangle, and Beyond)
This is the general-purpose method that handles almost any irregular shape: break it into pieces you already know how to calculate — usually rectangles and triangles — find each piece’s area, and add them together.
\(\text{Total Area}=\text{Area}_1+\text{Area}_2+\text{Area}_3+...\)
Section C practices this directly with rectangle-plus-triangle combinations — a house shape, a rectangle with one triangular end, and a rectangle with triangles on both ends.
A Few Mistakes Worth Watching For
Forgetting to add every piece is the most common one — labeling each section with a letter (A, B, C) before calculating keeps track of what’s left. Mixing up which side is the base and which is the height in a triangle is another. And for notched-rectangle problems like Section B, subtracting the wrong corner — or forgetting to subtract at all — throws the whole answer off.
Frequently Asked Questions
Trace the shape onto a grid, then count squares: full squares count as 1, squares more than half covered also count as 1, squares about half covered count as ½, and anything less than half is ignored. Add up the count for the total estimated area.
Use the sides you do know to work out the missing one first. In a rectilinear shape, sides running the same direction have to add up to match the outer dimension — for example, if the outer width is 10 and a notch is 4 wide, the remaining segment must be 6.
Yes. Use the Print / Save as PDF button above — it opens your browser’s print dialog, where you can choose ‘Save as PDF’ as the destination instead of a physical printer.
Yes. Click Show Answers to reveal every problem’s solution with the full working shown, or print the page — the answers are included automatically in the printed version.
These problems suit upper elementary through middle school — roughly the level where students first learn to decompose shapes into rectangles and triangles to find area.
Bottom Line
Splitting a shape into rectangles and triangles gets you most of the way there. Knowing what to do when a side is missing, and how to count a grid properly, gets you the rest of the way. Work through all nine, check your answers, and both gaps close fast.
