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Maths year 11

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Original post by hamza772000

Hey, I know you didn't ask me, but I just saw this question so I tought I'd help. :smile:

The answer is 80, not 50. You've figured out the fact that two base angles in an isoceles triangle are equal, but the one's you think are the same, actually aren't. Angle FEB and EBF are the same. Angle EFB isn't 50 degrees because the BASE angles are the same, in this case the base is EB.

So if you know that Angle FEB and BEF are 50, then Angle BFE would equal 80, because 180-(50+50)=80.

Angle x is alternate to Angle EFB therefore it must also be 80 degrees. :smile:

Don't understand!!!
Can someone please draw this out."(

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Reply 421

z_o_e

I got it. But I don't understand how BE is the base?

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Reply 422

username2437011

Original post by z_o_e

I got it. But I don't understand how BE is the base?

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I meant the line BE. B to E because both angles are the same, 50 and 50, so it is the base.

Reply 423

B_9710

Original post by z_o_e

I got it. But I don't understand how BE is the base?

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You should see that BE is the base and that BF and EF are the same length. (The image has rotated but you should still be able to see what I mean clearly enough).

Reply 424

z_o_e

Original post by B_9710

You should see that BE is the base and that BF and EF are the same length. (The image has rotated but you should still be able to see what I mean clearly enough).

OOOOOOH THANK YOU SO MUCH ♥

STUPID ME.

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Reply 425

z_o_e

Original post by B_9710

You should see that BE is the base and that BF and EF are the same length. (The image has rotated but you should still be able to see what I mean clearly enough).

Wb this

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Reply 426

B_9710

Original post by z_o_e

Wb this

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Area of trapezium is

\frac{1}{2} h(a+b)

, where h is the distance between the parallel sides and a and b are the lengths of the parallel sides (alternatively you could split it up into a rectangle and a triangle). Then find how many bags will need to be bought to cover the area of the garden.

Reply 427

z_o_e

Original post by B_9710

Area of trapezium is

\frac{1}{2} h(a+b)

Do you mean something like this?

Or a square and triangle?

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Reply 428

B_9710

Original post by z_o_e

Do you mean something like this?

Or a square and triangle?

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Yeah if you look at the top diagram, you have split it into a rectangle and triangle, both of which you can easily find the area of.

Reply 429

z_o_e

Original post by B_9710

Yeah if you look at the top diagram, you have split it into a rectangle and triangle, both of which you can easily find the area of.

What about the triangle the base?

It can't be 18?

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Reply 430

B_9710

Original post by z_o_e

What about the triangle the base?

It can't be 18?

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It is the long side - short sides = 18-12=6.

Reply 431

RDKGames

Study Forum Helper

Original post by z_o_e

What about the triangle the base?

It can't be 18?
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Why did you split the rectangle into 2 different rectangles?? There is no need, simply split the trapezium into a right-angled triangle and a rectangle. The bottom length will be split into a 12 and a 6 because the 12 matches the top side of the rectangle, and the 6 just adds on to make up the 18. Now you have a rectangle with area 12x9=108 and a triangle with area (6)(9)/2=27. Adding both of these will give you the entire area which is 135.

For the price, divide the 135 by 20 in order to see how many bags you need. Obviously you cannot have 6.75 bags so you will need to round up in order to ensure that it is an integer amount of bags as well as they are able to cover the whole trapezium. So 7 bags. Price would be 7x4.99 and there you have the answer.