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Fraction Classroom · 2.3.0 · Student pages

Split an L-shape into non-overlapping rectangles

Find the area of a composite shape by choosing parts that cover it once, then check the result with a second decomposition.

Anonymous group code: __________   Date: __________

Each cell is one square unit. The upper-right 2-by-2 corner is absent; the dotted boundary shows the containing 6-by-4 rectangle.6 units across; 4 units tall
Each cell is one square unit. The upper-right 2-by-2 corner is absent; the dotted boundary shows the containing 6-by-4 rectangle.

Build the idea

model. An L-shape starts as a 6-by-4 rectangle with a 2-by-2 corner removed from the upper right. What is its area?

  1. Locate the missing corner before calculating. Its width is 2 units and its height is 2 units; it is not part of the covered shape.
  2. Draw a vertical line where the missing corner begins. The left part is 4 by 4, while the lower-right part is 2 by 2.
  3. Add the two non-overlapping areas: 4 × 4 + 2 × 2 = 20. Check that every remaining unit square belongs to one part.
  4. Check another way: the full 6-by-4 rectangle has area 24, and the missing corner has area 4. Removing it also leaves 20 square units.

Worked example: 20 square units. Split the remaining shape into a 4-by-4 rectangle and a 2-by-2 rectangle: 16 + 4 = 20.

Practise and explain

Try p1–p3 with a partner. Use a drawing and label your units. Try e1 independently before comparing responses.

p1. An L-shape is a 5-by-4 rectangle with an upper-right 2-by-1 corner removed. Find its area in square units.

p2. Two non-overlapping rectangles, 3 by 4 and 2 by 2, join along an edge. Find their total area in square units.

p3. An 8-by-3 rectangle loses a 2-by-2 corner. Find the remaining area in square units.

e1. Draw a 7-by-5 rectangle with a 3-by-2 corner removed. Find the L-shape area and show a valid decomposition.

Transfer the idea

transfer. A learner draws two rectangles that overlap in one unit square and adds their areas. How should the count be repaired?