We assume that the cement path is of equal width at any point on the path.
6 years ago
Edlynn Rose
1. Find the area 60x60.
2. Find the area 60x42 (path removed).
3. Subtract (2) from (1) to find area of cement path.
6 years ago
Zhong Shu Hao
If so,
Area not covered by cement = 60m x (60m-18m)
= 60m x 42m
= 2520m^2
Area of cement path = 60m x 60m - 2520m^2
= 3600m^2 - 2520m^2
= 1080 m^2.
6 years ago
Caroline Lim
Thanks Zhong Shu Hao!
6 years ago
Yeo Robert
I dont think there are any correct answers.
Insufficient information given.
6 years ago
Zhong Shu Hao
So thats why I say....We assume that the cement path is of equal width at any point on the path.
6 years ago
Zhong Shu Hao
PSLE math and science actually invovles quite a lot of assumptions....
6 years ago
Yeo Robert
Even with equal width .... there are still no correct answer. Unless the path length is measured.
6 years ago
Zhong Shu Hao
HUH?
6 years ago
Yeo Robert
The answer 60m times 18 m is assuming the path is striaght and perpendicular to the sides.
6 years ago
Zhong Shu Hao
Just shift the diagram like this
6 years ago
Raymond Ng
Ans: 60 x 18 = 1080, regardless of whether path is linear or not, so long as it doesn't "loop" back ie no overlap.
Assuming path is of constant width throughout
6 years ago
Leonie R Tan
I feel this is not a very good question. It's a curve line, not straight line.... How to assume that it straightens to a straight line (60-18)?
6 years ago
Raymond Ng
Leonie R Tan, relax... this is a P6 Question, not NUSH Year 6 question.
I have tried to explain using P6 logic. I can prove it to you using calculus. You want? ☺
6 years ago
Raymond Ng
Another P6 logic. Try to imagine 2 containers: one is cylinder diameter 18cm, another is the curvilinear shape like above, constant but curvilinear width of 18cm. Both same height of 60cm.
If you pour water to their brim, who has more water??
6 years ago
Leonie R Tan
It's ok Raymond. I am sure u can prove that the curve line is equal straight line.:) just that I find it's too much assumptions for the kids to make. Based on what I have seen in some school papers, I think there are many other area questions that can be set to test the kids, and within better parameters of assumptions.
6 years ago
Raymond Ng
Correction. The curve is much longer than the straight lines (if drawn). Just that they cover the same area ☺
6 years ago
Raymond Ng
My take on this question is this: This is a profound yet giveaway question. I mean if I'm the student, seeing only 18cm & 60cm, I don't have better knowledge of what to do, I'll just treat it like a rectangle & multiply the 2 numbers & bingo! Got the right answers...
6 years ago
Helen Soh
Based on the picture.. The wave look uniform.. If draw 2 straight line..
6 years ago
Bridget McGivern
I have to admit I didn't see this at first but my friend said "If you were to cut the path horizontally, and slide the lower part up, it would nest. That would then form a rectangle." The rectangle would measure 18x60 square meters. So Raymond is right!
6 years ago
Yeo Robert
The assumption is that you could draw two straight lines that are perpendicular to the sides of the square ..... the diagram looks like that but it was not clearly labelled it is like that ...
6 years ago
Raymond Ng
Oh heng ah... so I'm right... yea...😭
6 years ago
Chip Rollinson
assuming a constant width, use Cavalieri's Principle to get the area of the path 18x60=1080 sq m.. what's Cavalieri's Principle? Either read the Wikipedia entry or check out this site: http://www.pbslearningmedia.org/resource/geometry-cavalieri-2d/cavalieris-principle-in-2d-school-yourself-geometry/
6 years ago
Yeo Robert
Let me illustrate what an exaggerated picture might look like if the lines are not perpendicular to the sides .... here the path is made up of two 1/4 circular tracks. The height of the picture has been changed to longer than 60 meters ..... the width is still 60 meters ... and the width of the path is still 18 meters ..... the area of the path in this case is much bigger than 18 x 60 ....
6 years ago
Raymond Ng
Robert Yeo, you've just violated my "no loop back" rule...😭
6 years ago
Khew Su-Lyn
Area of whole sq = 60 x 60 = 3600, Area of non cement = 60 X (60-18) = 2520, Therefore area of cement = 3600-2520 = 1080
6 years ago
Helen Soh
I am thinking whether symmetry n tessellation applies..
6 years ago
Yeo Robert
the question never said that was no loop back ....... the graph shows a constant width of 18 meters by one definition ... and another width by another definition ...... so the question is still not clear ... just my personal opinion ......
6 years ago
Yeo Robert
And it is loop sidesways ... there was no loop back .... ok..... sorry i am just being anal about the definition of loop back ...... (But I get what you mean .....)
6 years ago
Yeo Robert
Different people have different definition of width of the path ... I take it to mean the perpendicular width of the path ..........
6 years ago
Pedro Cferreira
Remembers me Bonaventura Cavalieri. He explains that in a very easy way.