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UKMT Question

I'm just looking over some maths challenge questions and since I'm awful at geometry based stuff I can't see a way to do this. I know what the answer should be, but if someone could show a decent method that'd be great.

T is 4
87fb2822a82944f28765b2cccd510628.png

Answer:

Spoiler

Original post by Bruhh
I'm just looking over some maths challenge questions and since I'm awful at geometry based stuff I can't see a way to do this. I know what the answer should be, but if someone could show a decent method that'd be great.

T is 4
87fb2822a82944f28765b2cccd510628.png

Answer:

Spoiler




We need the value of T.

What have you got so far?
Reply 2
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Bruhh
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10
Original post by Muttley79
We need the value of T.

What have you got so far?


I put that in the OP, T is 4.
Original post by Bruhh
I put that in the OP, T is 4.


Sorry, I missed it -

What have you tried?

We know the area of the trapezium and something about the two parallel sides so ...
Reply 4
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Bruhh
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Original post by Muttley79
Sorry, I missed it -

What have you tried?

We know the area of the trapezium and something about the two parallel sides so ...


Well I have (3*AE*h)/2 = 27 where h is the height of the trapezium

I'm not sure how to use the fact F is the midpoint, other than that CF=BF obviously.
Original post by Bruhh
Well I have (3*AE*h)/2 = 27 where h is the height of the trapezium

I'm not sure how to use the fact F is the midpoint, other than that CF=BF obviously.


OK so we can say Ah = 18?

Then find the area of each of the triangles ...[think about the heights of the two on the right]

Then subtract from the area of the trapezium.
Reply 6
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Bruhh
OP
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Original post by Muttley79
OK so we can say Ah = 18?

Then find the area of each of the triangles ...[think about the heights of the two on the right]

Then subtract from the area of the trapezium.


Ah yes I've got it! Thanks for that.
Original post by Bruhh
Ah yes I've got it! Thanks for that.


You could also look at the fraction of the trapezium shaded.

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