The idea in brief. Adding identical overlapping shapes counts their shared part twice. The figure contains that part once, so one copy comes off. The two pieces sticking out are equal because each is one identical shape minus the same shared part. In the lesson. The difference between them is one shared part.
Lesson video, with the working
Two shapes overlap
4 min 12 s
The film teaches 3 questions in turn. Each question shows first; its working is written as the film explains it.
Two identical squares of side 10 cm overlap. The part where they overlap is a square of side 4 cm. Find the area of the figure the two squares cover.
Area covered = 100 + 100 − 16 = 184 cm²
Ans: 184 cm²
Example 1
Two identical right-angled triangles overlap. Each triangle has a base of 16 cm. Its height is 12 cm. Together they cover an area of 150 cm². Find the area of the part where the two triangles overlap.
Area of the overlap = 192 − 150 = 42 cm²
Ans: 42 cm²
Example 2
Triangles ABC and STU are identical right-angled triangles that overlap. Each triangle has a base of 20 cm. Its height is 8 cm. The two shaded parts are outside the overlap. Their total area is 100 cm². Find the area of the unshaded part where the two triangles overlap.
Area of the overlap = 80 − 50 = 30 cm²
Ans: 30 cm²
How to solve it
Find the piece the two shapes share. Area covered is both shapes minus one shared part.
Find the area of one whole shape: 10 times 10 is 100 square centimetres.
Find the area of the shared piece: 4 times 4 is 16 square centimetres.
Add the two shapes, then take off the shared part once: 100 plus 100 minus 16 is 184 square centimetres.
To find the overlap instead, work backwards: the two triangles minus the area covered, 192 minus 150, is 42 square centimetres.
A shared piece is inside both shapes. On the paper, a shared piece is there once. In the sum, a shared piece is there twice. The difference between them is one shared part.
Practice questions with worked solutions
Question 1 is free to try. The other 9 open in the free trial, each with its full working.
Question 1 of 10 · Basic · free to tryBala glues two identical rectangular strips of card, each 18 cm by 6 cm, at…Bala glues two identical…
Bala glues two identical rectangular strips of card, each 18 cm by 6 cm, at right angles to make an L-shaped label. The label covers 180 cm² of the notice board. Find the area of the part where the two strips overlap.
How do you solve overlapping shapes questions in P6?
Overlapping shapes questions put two identical squares, rectangles or triangles on top of each other and ask for the area they cover, the shared part, or a length.
What your child learns here
Overlapping shapes questions put two identical squares, rectangles or triangles on top of each other and ask for the area they cover, the shared part, or a length. They sit under the Primary 6 outcome on the area of composite figures.
Find the area of each whole shape, using area of square, rectangle and triangle.
Find the part the two shapes share, and see that it belongs to both of them.
Find the area covered: both shapes added, then the shared part taken off once.
Work backwards: both shapes minus the area covered gives the shared part, and a known area with one side gives a missing length.
Does the answer make sense?
When the answer is the area the shapes cover together, it must be less than all the whole shapes added but more than any one shape alone. When your child finds the shared part, it must be smaller than one whole shape, since it sits inside each of them.
How to practise these questions
The Basic questions train the central idea that the shared part is counted only once when two shapes cover an area together. Intermediate questions add working backwards from the covered area to the overlap, or on to a length. Challenge questions describe the overlap as a fraction, use three shapes with two overlaps, or end with a height. When the overlapping area seems counted twice, read the written step-by-step solution.
Questions parents ask
Is overlapping shapes in the PSLE syllabus? The Primary 6 syllabus includes finding the area and perimeter of composite figures made up of squares, rectangles, triangles, semicircles and quarter circles. Overlapping shapes are one kind of composite figure, so they sit within that outcome.
Why is the shared part taken off only once? Adding the two shapes counts the shared part twice, once inside each shape. On the paper it is there once, so one copy comes off.
How does my child find the area of the overlap itself? Work backwards: add the areas of the two shapes, then subtract the area they cover together. What is left is the shared part.
