The shaded part for 1 single triangle is $4/9$ths of the total area of the triangle. If this was considered to be 4 units, then the unshaded $5/9$ths would be 5 units. Thus the total area of the whole figure is 14 units and so $4/14$ths or $2/7$ths are shaded.
I believe that's the right answer, but can someone tell me is there a more efficient or a method that utilises geometry?
Thanks
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$\begingroup$Here’s a quick visual way of thinking that I would expect a 10- or 11-year-old to be capable of.
No arithmetic beyond counting nor a single word nor any spare space is necessary. (I presume expect that students are permitted to draw on or annotate their examination papers.)
(Each dot represents what we would call a unit of area.)
$\endgroup$ 1 $\begingroup$Do not worry. This is without doubt the easiest and fastest approach to solve this question.
So I feel like there is some assumed knowledge that I'm omitting
Mathematics is full of known results and equations, but you can't have known results for literally everything! :)
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