1. ## Up to a trigonometry puzzle ?

Ok so my daughter has this puzzle as part of an assignment in math...
The original puzzle is a bit more complex involving... a goat (don't ask) but I reduced it to the below: calculate the area in red color.
Inner circle has a radius of 3cm.
Outer circle has a radius of 4cm.
One important piece of information is that we are not allowed to express angles as a fraction of Pi.

I'm frustrated . @cendrillon  Quote

2. Is this a variation of one of those box in a circle problems and is the answer 5.56cm^2?

Where you use Pythagoras and take 4^2 - 3^2 and you get 7^0.5 and solve that the area of the (imaginary) box is 28 then subtract from the circle with a 4 cm radius to get an area of 50.24 (3.14*4^2) then take the resulting figure of 22.24 and divide by 4?  Quote

3. If the area is 3.63cm.sq, you can try calculating the area of segment from area of sector minus area of triangle. For area of sector, u need the angle, which u can get thru Pythagoras principle.  Quote

4. You beat me to it @shafiq - I got the same result as you 3.628

https://www.mathopenref.com/segmentarea.html  Quote

5. Apologies I should have mentioned as well that my daughter hasn't learnt sin/cos yet.
@Viktri yes I think this is what you're trying to say, I was not aware of these puzzles.

Basically we substract the area of the box in green to the area of the big circle, and divide by 4 to get the area of the segment in red.

It's one of those puzzles where you need a good pair of eyes more than a brain.

(3.14x4^2 - 3^2)/4=10.31   Quote

6. Originally Posted by jrkob
Apologies I should have mentioned as well that my daughter hasn't learn sin/cos yet.
@Viktri yes I think this is what you're trying to say, I was not aware of these puzzles.

Basically we substract the area of the box in green to the area of the big circle, and divide by 4 to get the area of the segment in red.

It's one of those puzzles where you need a good pair of eyes more than a brain.

(3.14x4^2 - 3^2)/4=10.31 This will be stored in case something like it comes up in my kids' homework and I can then impress them with my intelligence!  Quote

7. Originally Posted by jrkob
Apologies I should have mentioned as well that my daughter hasn't learnt sin/cos yet.
@Viktri yes I think this is what you're trying to say, I was not aware of these puzzles.

Basically we substract the area of the box in green to the area of the big circle, and divide by 4 to get the area of the segment in red.

It's one of those puzzles where you need a good pair of eyes more than a brain.

(3.14x4^2 - 3^2)/4=10.31 Side of square is 6 or 3?.
Area should be 3.6 either way?  Quote

8. Outer circle - Pi x 4 x 4 = 50.24
Inner Square - 6x6 = 36
Arc = (50.24-36)/4 = 3.56 = 3.6  Quote

9. Oops yes I posted a bit quick and before my first coffee.
3.6
@hullexile I'll post the entire worksheet tonight when I'm home. The puzzles then get more complicated   Quote

10. I'm only here for the goat  Quote