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## Jaxson

6448 posts

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108m^2 is the total area of the whole shape.

Regardless of being a square or not, it's areas is still one side multiplied by the other.

It's shown close to a square in the demo drawing, so not enough to get worked up over.

## eracode

2245 posts

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LennonNZ: long story.. but..

12 and 36

Lets work it out..

Rectangle and Triangle

d(12−0.5d)+2(0.5(0.5d(0.5)d))=108
−0.25d2+12d−108=0

Use some quadratic formula (a little hard to display here)

d=12 and 36

Of course the image is nothing like that the imaginary shape as the triangle has a negative size or the rectangle does.

(or I got it complete wrong) :-)

The solution of the quadratic equation

d^2 - 48d + 432 = 0

which represents the total area of 108 m2, is:

(d - 36)(d - 12) = 0

and therefore d = 36 or 12.

## eracode

2245 posts

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2 people support this post

F*** you Envelope. I never liked letters anyway.

## evnafets

72 posts

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3 people support this post

And to finish off stating the obvious.  The equation has solutions of d = 12, or d = 36

However you can also determine from the diagram, the constraint of 12 - d/2 > 0.
Using d = 36 gives you a negative result for that equation, therefore d=12 would be the correct answer for this question.

1380 posts

Uber Geek

Jaxson:

108m^2 is the total area of the whole shape.

Regardless of being a square or not, it's areas is still one side multiplied by the other.

It's shown close to a square in the demo drawing, so not enough to get worked up over.
i added the statement for clarity. Some people get worked up over nothing ...

## Kyanar

2915 posts

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2 people support this post

"That exam wasn't there to test us, it was to trick, no one could of prepared for that," another VCE student wrote.

This student should probably spend a bit more time studying at school, rather than complaining about the content.

## hashbrown

434 posts

Ultimate Geek

Subscriber

I suspect the envelope problem is a good question that got mangled. If you make the bottom side of the "square" 12-d/4, the d^2 terms cancel and you are left with 12d=108, so d=9. As an added bonus the "square" is now 9x9.75 which is believable for the way it was drawn.

Obviously the total length is now 12+d/4, but it was weird they gave you that redundant info in the first place.

## Sideface

3625 posts

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Subscriber

andrew027:

I thought that this was a silly question until I saw this:

Suzuki Microbus-like van

Sideface

## PeerCover

6 posts

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Inactive user

I briefly read the article but then realized it was an Australian 50 cent coin. I think referring to Australian currency really threw the Australian students. After all, how can one make sense of the \$2 being smaller than \$1, the 20 cents being bigger than both the dollars and the 50 cents being the biggest of all the coins. It defies logic. Now they want students to apply geometry to these illogical manifolds - tough ask!

## andrew027

1215 posts

Uber Geek

One person supports this post

PeerCover: I briefly read the article but then realized it was an Australian 50 cent coin. I think referring to Australian currency really threw the Australian students. After all, how can one make sense of the \$2 being smaller than \$1, the 20 cents being bigger than both the dollars and the 50 cents being the biggest of all the coins. It defies logic. Now they want students to apply geometry to these illogical manifolds - tough ask!

But the NZ 50c is bigger than the NZ \$1 coin so size is not necessarily relevant.

I was living in Australia when the \$2 coin was first issued in 1988 - I remember a nice cartoon of then-treasurer Paul Keating explaining to a reporter that the \$2 was smaller than the \$1 because two dollars was worth less in 1988 than one dollar was in 1984 (when the \$1 coin was released).

And the old joke why a UK 50p coin is shaped the way it is - so you can use a spanner to remove it from a Scotsman's hand.

## Kiwifruta

604 posts

Ultimate Geek

andrew027: I still remember from high school geometry (and it has been 38 years since I did high school geometry) that the exterior angles of a polygon add up to 360°. The 50c piece has 12 angles, so 360÷12=30. There are two 50c pieces side-by-side, so the angle at the point the two coins meet is 2×30=60°. For kids who should have learned this stuff within a year or two of sitting the exam, I'm surprised at all the fuss it has created.

I think the fuss reflects the sheer amount of people who did not pay attention during maths class. Fairly basic geometry question.
Personally, I think the question would have been better without multi choice to take away the 'look at the picture and take an educated guess as to what the angle looks like'.

## gzt

8995 posts

Uber Geek

8 sided polygon gives a direct answer, but method one was my first choice.

## Batman

16950 posts

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Trusted

Missus says (the other day) angle of the something something = 360/number of sides of polygon, x2.
wow ... who's the smart one in the family!

ok i can't remember her exact formula ... but sometihng like that. i will ask her again at some stage ..

ok i think that was right. whatever! lol

## gzt

8995 posts

Uber Geek

gzt: 8 sided polygon gives a direct answer, but method one was my first choice.

Oh wait I had that confused with a six sided regular polygon. : (.

## Kiwifruta

604 posts

Ultimate Geek

joker97: Missus says (the other day) angle of the something something = 360/number of sides of polygon, x2.
wow ... who's the smart one in the family!

ok i can't remember her exact formula ... but sometihng like that. i will ask her again at some stage ..

ok i think that was right. whatever! lol

where n is the number of sides
180-360/n, which can be rearranged to 180x(1-2/n)

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