Geometry and measurementGrades 3–6
Area of irregular shapes worksheets
Prints L, T, U and step-shaped figures with every side labeled. Students split each into rectangles and add the areas. You can ask for area, perimeter or both, and hide some side lengths. Key included.
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On this page
Cutting a hard shape into easy ones
An irregular shape here means a figure with only right angles but an outline that is not a plain rectangle. Letters give the best-known examples: an L, a T, a U, or a staircase. Nobody has a formula for those, and that is the point. Students learn that area can be added, so a shape with no formula can be cut into rectangles that do have one.
The sheets suit grades 3 to 6. Children who can already find the area of a rectangle by multiplying are ready. Afterward, they can move to triangle area, where the pieces are no longer rectangles.
What gets printed
Each page holds shapes in two columns, with the count set by Number of problems (2 to 12). Every figure is drawn from whole-number side lengths, with units chosen from centimeters, meters, inches and feet. The four outlines (L, U, T and step) appear in a mix, and each side carries its length beside it. Below the figure is a blank for the answer.
The instruction line tells students to split the shape into rectangles, find the area of each, then add, and to write square units.
Choosing the settings
- Find. "Area" is the main skill. "Perimeter" asks them only to add the sides. "Area and perimeter" prints two blanks, A and P, which is a good way to separate the two ideas that children often mix up.
- Some side lengths missing. Off, every side is labeled. On, two sides show a question mark, and the student first works out those lengths from the sides opposite them. This is a real step up and adds the skill of reasoning about parallel sides.
- Number of problems. Six is a comfortable page. Four is enough for a first try with missing sides.
Worked example: an L-shape 12 cm wide and 9 cm tall
Picture an L whose bottom bar runs the full 12 cm wide and is 5 cm tall. The upright part on the left is 7 cm wide. The outline sides, going around, are 12, 5, 5, 4, 7 and 9 cm.
Area, by splitting:
- Cut the shape with a horizontal line. The bottom piece is 12 cm by 5 cm: 12 × 5 = 60 cm².
- The top piece sits above it, 7 cm wide. Its height is 9 − 5 = 4 cm. So 7 × 4 = 28 cm².
- Add: 60 + 28 = 88 cm².
Check by subtraction. The whole 12 by 9 rectangle is 108 cm². The missing corner is 5 cm wide and 4 cm tall, so 20 cm². And 108 − 20 = 88 cm².
Perimeter: 12 + 5 + 5 + 4 + 7 + 9 = 42 cm. This equals 2 × (12 + 9) = 42, because an L's outline is as long as the box around it.
Mistakes the key will show
- Perimeter instead of area. The answer lacks square units or is far smaller. Check that the unit has a small 2.
- Overlapping pieces. The student counts the corner twice, so the total is too high. Draw the cut line and label each piece.
- Using a label that is not a piece's side. A 12 cm outer width is not the width of a top piece that is only 7 cm wide.
- Missing sides guessed. When some lengths are hidden, a student sometimes copies a nearby number. Ask which two labeled sides add up to the unknown one.
With the hidden-sides option on, the generator hides at most one side running across and one running up and down, so every missing length can be found from the labeled sides parallel to it.
Teaching tip
Have students try two different cuts on the same shape and compare totals. Getting 88 both ways is more convincing than any explanation. For more practice with multiplying in each piece, the 2-digit multiplication worksheets help, and surface area and volume carry the same adding-of-parts idea into 3D.