Two identical figures overlapping is in the Primary 5 Area of Triangle chapter. The lesson film is the one Mathweave teaches this skill with in Primary 6, and the practice set below is chosen for Primary 5.
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 of 2
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 of 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 8 open in the free trial, each with its full working.
Question 1 of 9 · Basic · free to tryTwo identical rectangles, each 15 cm by 8 cm, are laid across each other so…Two identical rectangles, each…
Two identical rectangles, each 15 cm by 8 cm, are laid across each other so that the part where they cross is a square of side 8 cm. Find the area of the figure the two rectangles cover.
How do you solve overlapping shapes area questions in P5?
When two identical rectangles, squares or right-angled triangles overlap, the piece they share is covered by both of them.
What your child learns here
When two identical rectangles, squares or right-angled triangles overlap, the piece they share is covered by both of them. This page uses the Primary 5 outcomes on the area of a triangle and on composite figures to count that shared piece exactly once.
Find the area of one shape, then double it for the two identical shapes.
Adding the two shapes counts the shared part twice, so subtract it once to get the area covered.
To find the shared part, subtract the area covered from the two shapes added together.
To find a length, rebuild the area of one shape first, then divide by the side you know.
The parts outside the overlap are equal in area, because the two shapes are identical.
Does the answer make sense?
Each rectangle is 15 × 8 = 120 cm², so the two together make 240 cm². The covered figure must be less than 240 cm², since that sum counts the 64 cm² square twice, and more than the 120 cm² of one rectangle. 240 minus 64 is 176 cm², which sits between the two.
How to practise these questions
Free Question 1 lays two 15 cm by 8 cm rectangles across each other so that they cross in a square of side 8 cm, and asks for the area of the figure they cover. The Basic questions train the rule of adding both shapes and subtracting the shared part once, with rectangles, squares and tiles. Intermediate questions work backwards to the overlap or a breadth, or find the area two triangles cover. Challenge questions bring in three cards, shaded parts outside the overlap, and an overlap that is a quarter of each square. If your child is stuck, open its worked solution and shade the shared part before adding.
Questions parents ask
Why is the overlap subtracted only once? The shared part belongs to both shapes, so it sits inside each of the two areas that were added. On the paper it is covered once, so one copy comes off and one stays.
How do you find the area of the overlap? Add the areas of the two shapes, then subtract the area the whole figure covers. What is left is the shared part, the piece that was counted a second time.
Are overlapping circles part of Primary 5? No. Circles are a Primary 6 topic. The Primary 5 questions here overlap rectangles, squares and right-angled triangles only.
