maths homework - geometry

[kags]

my son has been asked to calculate the volume and surface area of a triangular prism. The base is a right angled scalene triangle, the sides adjoining the right angle being 200cm and 50cm. The hypotenuse is not given. The prism is 300 centimetres long. He has calculated the volume as 200 x 50 x 300 divided by 2, which I think is correct. However, to calculate the surface area he needs the length of the hypotenuse, to calculate the area of the side of the rectangular side of the prism. He is absolutely adamant that he has not been taught Pythagorus, and therefore would not be expected to know it - I don't think he can do the calculation without it! Am I missing something?

[Buenchico]

I taught maths for 15 years.

Assuming that your son's school isn't tackling the syllabus in a very unorthodox manner (so that he could use trigonometry to help him find the length of the hypotenuse) the only method I can think of is scale drawing.

i.e. using a 1 to 10 scale, draw a right-angled triangle with (non-hypotenuse) sides of 20cm and 5cm. Measure the hypotenuse and then scale up to the 'real' measurement, by multiplying by 10.

If your son is of average ability (and hasn't yet covered Pythagoras), his maths teacher should be shot for setting such a lousy question. However, if your son is a high-flyer, his maths teacher is to be praised for creating a challenge for pupils.

Chris

[Naomicorlett]

Agree with calculation on volume 1,500,000 cubic cm . using square root of sum of squares of two sides of right angle gives a hypotenuse of 206.155281. Are you sure about question ? It seems very hard

[Naomicorlett]

Ah 20cm not 200cm on one side .Thought it was big!!

[kags]

He has been recognised as gifted and talented in Maths, so I believe the intention is not to use scale drawings but trigonometry. My own memory from school is that Pythagorus was taught very early on trigonometry, but it seems that he genuinely has not been taught it. He knows it now, as I have just explained it to him, but as with most children he only believes it if the teacher has told him! I am glad you agree that Pythagorus is necessary here!

[kags]

Naomicorlett - actually it WAS 200 - and we got the same answer as you!

[Naomicorlett]

I used to use the 3/4/5 rule to understand how to work out pythagorus. eg. draw a triangle with those sides and if the other two sides are 3 and 4 then the hypotenuse is 5 . SO ......3 squared =9 plus 4 squared = 16 add them together =25 ...square root of 25 is 5 . it's just a simple way of remembering how to do it. Hope this helps.

[spacechimp]

Well, I doubt he's been taught sine and cosine if he's not been taught Pythagoras...

[Buenchico]

Well, I'm glad that we seem to have got there.

The simplest trigonometry approach is probably as follows:

Let the angle opposite the 50cm side be x

=> tan x = 50/200 = 0.25

=> x = 14.036 degrees (to 5 s.f).

We now have sin14.036� = 50/h, where h is the length of the hypotenuse.

=> h = 50/sin14.036� = 206.16 cm (to 5 s.f)

[Naomicorlett]

Kags, will you please let me know what method the teacher expected to be used. It's been bugging me all night ! I realise it prob wont be after the weeekend. Thank you Naomi

[kags]

I'll let you know as soon as he tells me - he's only 12 bless him!

[factor-fiction]

I calculate overall surface area to be 146847 cm�
I think most 16 year olds would fail to tackle this.
Pythagoras' theorem is unheard of nowadays to most secondary pupils

[spacechimp]

Think you're exaggerating a bit there factor30. I distinctly remember being taught Pythagoras' theorem in year 5.

[factor-fiction]

I'm afraid not spacechimp- it certainly isn't done before year 10 in most schools and unless you are doing Higher Tier Maths it may pass you by.

[spacechimp]

It may not have been part of the curriculum, but we watched a video where lots of happy children first constructed squares out of sheets of card on the shortest two sides of a right angled triangle, and then took these sheets to make one large square on the hypotenuse. (This is only 8 years ago).

Not until year 10? I hardly think so. I'm damn sure we were expected to know it for the Year 9 SATS, and probably for science as well as maths.

http://www.emaths.co.uk/sats/2007/68Paper2.pdf (see Q17 (c))

[Naomicorlett]

OOH is it maths tomorrow ? Can we have our answers marked please?

[kags]

he hasn't been to school yet this week because of the snow. He is curently exercising his mathematical brain by shooting people on Call of Duty.

[Naomicorlett]

And the score is ????

[Naomicorlett]

Are you still snowed in? would really like to know the method used. We haven't had any snow here but can see it on the mountain.

[kags]

We were back at school yesterday but the Maths teacher hasn't given them their homework back yet. Bit pointless after all this time i think, they will all have forgotten it anyway!

[Naomicorlett]

Kags...come on mark OUR homework. Did we get it right ? Doesn't it make you mad when teachers set homework and then don't mark it!!