#find an expression
winged veldt
winged veldt
I don’t know how to deal with the tiny corners where the circle fits into the rhombus
can someone help
bold hornet
make a line from the origin to the circumference (to make a 90
degree angle triangle)
let r = radius
area of circle= Pir ^2
area of rombus = 1/2 ab
looking at my triangle you will get a 90 right angled triangle and this triangle is inside another triangle with sides 1/2 a and 1/2 b, let the hypotenuse of the triangle be x
finding the area will be easier if we rotate the triangle as the formula for the area of a triangle is 1/2 bh
our base is our hypotenuse (x) and our height is the radius (r)
1/2 (x)(r)
1/2 xr
the rombus is 4 of these triangles if u look at the diagram so the area of the rombus is
4 x (1/2 xr)
which is 2xr
we have two expressions for our area of the rombus
1/2 ab and 2xr
we must find hyp in terms of a and b however so we do pythagoras on our triangle
root ((1/2a)^2 + (1/2b^2)
we get
×= 1/2 root a^2 + b^2
to find r we must do
1/2 ab = 2 r * (1/2 root a^2 + b^2)
since 2xr = 1/2 ab
ab = r (root a^2 + b^2)
rearrange for r
r= ab/2 (root (a^2 + b^2))
find expression for area of circle using r
area of circle = pi r ^2
= pi (a^2 b^2) / 4(a^2 + b^2)
final step is to find the ratio
we can do area of circle over area of rhombus using
area of circle = 1/4 pi (a^2 b^2) / (a^2 + b^2)
and area of rombus being 1/2 ab
divide them and u will get
1/2 pi (ab/ a^2 + b^2)
i can’t send the images for some reason
winged veldt
where did u get this q from it was quite interesting
idk tbh my teacher gave it
bold hornet
area of rhombus =
4 of these ^^ triangles
did u find out where this other q was from #1121869057428308040
bold hornet
kk
bold hornet
How can x be 1/2square root a^2b^2
pythagoras
a^2 + b^2 = c^2
a is (1/2 a) b is (1/2b)
root (1/2 a^2 + 1/2 b^2) gives us 1/2 root a^2 b^2
bold hornet
look at this
x is the hypotenuse
winged veldt
root (1/2 a^2 + 1/2 b^2) gives us 1/2 root a^2 b^2
it’s a^2 + b^2
bold hornet
it’s a^2 + b^2
yes that’s what i’ve done
i squared my value for a and value for b and added them to find c squared
c is the hypotenuse which is our x
bold hornet
it’s a^2 + b^2
wait yeah i typed it wrong
sorry for the confusion
it’s 1/2 root a^2 + b^2
bold hornet
make a line from the origin to the circumference (to make a 90
degree angle tria...
ok i corrected this
now check it
should make sense
gray mortar