Polygons

[proud mantle]

basically the regular hexagon is made up of six equilateral triangles

so 100cm^2 is equally divided between those six triangles, so 100/6 = roughly 16.6cm^2 of area per triangle

they used the formula 1/2 x ab x sinC, where angle C is between the sides A and B

the sides and a and b are x as all sides of an equilateral triangle are equal

and the angle between them is 60 degrees as every angle in an equilateral triangle is equal

so plug those into the formula

1/2 x^2 sin 6 = 16.6

then arrange for x, in which case x = sqrt[33.3/sin60] = 6.2cm

the topic of this should be trigonometry or cosine/sine rules or area of shapes

[marble pivot]

oh ok that makes so much sense

[proud mantle]

no problem

[marble pivot]

I knew it all just didn't realise it was the formula for area of a triangle 💀

[novel hearth]

have a look at that circle question that came up as a last q on last years gcse paper

it’s the same concept

[marble pivot]

edexcel?

[novel hearth]

yh

[marble pivot]

ok

will look it up

[novel hearth]

jus google hard circle q gcse

should be something about radii 4cm

[novel hearth]

u need to think a bit deeply to solve it

(area of sectors and triangles)

[marble pivot]

?

this

[marble pivot]

how is that a gcse question

[proud mantle]

it was in the 2022 gcse maths paper 1 exam for edexcel but it's difficult but not so much once you get it

[marble pivot]

i am trying it rn with small hints

didn't know a equilateral triangle formula existed👍

[river crane]

its christmas

[marble pivot]

yes merry chirtsmas

to you