This free printable helps learners calculate the area of an L-shape by subtracting a rectangular corner, then work backward to find a missing length. It includes a complete student worksheet and a separate worked answer page, with original diagrams and checked solutions.
Who this worksheet suits
Learners should already know that a rectangle’s area is length times width. The worksheet connects that familiar rule to a composite shape, keeping all dimensions in centimetres and all area answers in square centimetres.
What is on the student page
A worked diagram shows a six-by-five rectangle with a two-by-three corner removed. Three practice diagrams ask for shaded areas. A fourth reverses the calculation: the shaded area is given, and the learner must find the height of the missing corner. A final reasoning prompt compares the shape with its enclosing rectangle.
Teach the first example
Start by tracing the dashed outer edges to visualize the whole rectangle. Then outline the missing corner and identify its two dimensions. Let the learner write the two rectangle calculations separately before subtracting; this helps prevent the cutout dimensions being mixed with the outer dimensions.
Check a worked result
The teaching example gives thirty square centimetres for the whole and six for the cutout, leaving twenty-four. In question one, the same method gives 8 × 6 − 3 × 2 = 42 square centimetres. The reverse problem has a twelve-square-centimetre cutout, whose width is three centimetres, so its height is four.
Common mistakes to discuss
Some learners subtract the side lengths before multiplying, which creates a different rectangle. Others give a length unit for an area. Ask them to shade the missing corner in a second colour on a spare copy, label the two area calculations, and explain why the shaded L-shape must be smaller than the whole.
Worked answer key
Use the second page after an independent attempt. Compare the reasoning as well as the final answer. For explanation questions, equivalent clear wording is acceptable.
Download and print both pages
All required dimensions are printed beside the diagrams. Calculate from those labels rather than measuring the picture. Uniform fit-to-page scaling for Letter or A4 therefore preserves the answers. Use Download image beneath each page for its original 2550 × 3300 PNG at 300 dpi. Choose US Letter or A4 and Download PDF for that page. Download the student sheet and answer key separately. These are flat printables for handwriting, not interactive forms. Original pages are for personal and classroom use; share this article link when recommending them.