To find the total area covered by two overlapping rectangles, add their areas and subtract the overlap once. Each rectangle’s area already includes the shared region, so adding the two counts that part twice.
This PSLE Mathematics example uses two crossing strips. It shows how to find the area covered and how the working changes if the question asks for the area covered by exactly one strip.
- Find the area of each whole rectangle.
- Mark the region shared by both.
- Subtract the shared area once for the total covered.
- Read whether the question asks for all covered space or exactly one layer.
CHAPTER 1 OF 4 · Back to contents
Mark the shared rectangle
Draw a horizontal strip 12 cm long and 4 cm wide. Draw a vertical strip 10 cm long and 3 cm wide crossing the first strip completely at right angles. The overlap measures 4 cm by 3 cm. Its sides come from the widths of the two strips.
CHAPTER 2 OF 4 · Back to contents
Worked example | Find the area covered by either strip
The horizontal strip has area 12 × 4 = 48 cm². The vertical strip has area 10 × 3 = 30 cm². Together these figures give 78 cm², but that includes the overlap twice. Subtract 4 × 3 = 12 cm² once to obtain 66 cm².
Check by keeping the whole horizontal strip and counting only the vertical strip outside it. That part has area 30 − 12 = 18 cm². Adding 48 and 18 gives the same answer.
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CHAPTER 3 OF 4 · Back to contents
Change the question to “exactly one strip”
Now leave the overlap out entirely. The horizontal-only area is 48 − 12 = 36 cm² and the vertical-only area is 30 − 12 = 18 cm². The answer is 54 cm². The difference between the two answers is the 12 cm² that has both strips.
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CHAPTER 4 OF 4 · Back to contents
Frequently asked questions
What if the strips only touch at an edge?
A shared edge has no area, so add the two areas directly.
What can a parent ask before showing the answer?
Ask the child to point to the part included in both multiplications. Then ask whether the final answer should include that part once or leave it out.