#gcse maths - similar shapes

84 messages · Page 1 of 1 (latest)

shut swan
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yuck

fringe yew
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i dont get it

shut swan
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ok so

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just to be able to give names for things

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im just gonna call the area of the small middle cross A

fringe yew
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ok

shut swan
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so using the fact that the side lengths are 1 : 4 for small : medium cross

fringe yew
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ye

shut swan
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how might you write an expression for the area of the whole medium cross

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using A

fringe yew
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4a?

shut swan
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not quite

fringe yew
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ok

shut swan
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so do you rememver how

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length scale factor, and area scale factor

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link

fringe yew
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ye

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like you square them to move between them

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i think

shut swan
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exactly yes

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you square the length scale factor

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to get the area scale factor

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now what is the length scale factor between the small cross and the medium one

fringe yew
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4

shut swan
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so what can you

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deduce

fringe yew
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square it to 16?

shut swan
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perfect

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so if the area of the small cross is A

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whats the area of the medium?

fringe yew
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15A?

shut swan
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ah so

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so you removed the small cross havent you

fringe yew
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yes

shut swan
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yea so

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we can say that

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15A is the shaded area right

fringe yew
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yes

shut swan
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awesome

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now can you use that same idea and logic

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to connect the small cross to the large cross

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and again work out the areas

fringe yew
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ok is it

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10A?

shut swan
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not quite

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so im gonna say that the whole medium cross including the bit cut out

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is 16A right

fringe yew
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yes

shut swan
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so instead of taking 15A from the 25A you worked out

fringe yew
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take away 16?

shut swan
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yep

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so the outside unshaded bit is

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9A right?

fringe yew
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9

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a

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yes

shut swan
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awesome so

fringe yew
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so would it be 3:5

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if you divideby 3

shut swan
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not quite

fringe yew
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ok

shut swan
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so just to like track everything we found

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small cross is A and large outside cross is 9A

fringe yew
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yes

shut swan
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so the combined unshaded is 10A

fringe yew
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yes

shut swan
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right?

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and then we said before the shaded was 15A

fringe yew
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yes

shut swan
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so thats the ratio you wanna get from

fringe yew
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2:3?

shut swan
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other way round

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but yes

fringe yew
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ah 3:2

shut swan
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cuz its shaded : unshaded

fringe yew
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thank yo so much

shut swan
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but yeah perfect!

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no worries!

fringe yew
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you communicates better than any of my teachers using text

shut swan
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i mean i have a lot more practise doing maths over text than your teachers i reckon

fringe yew
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i mean when they actually teach in person

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like your explanation and step-by step is so good

shut swan
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oh thank you 😄

fringe yew
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no problem