What's the area of the shaded regions?

[Guest]

Someone claim that this is a question of primary school in China.Is that possible to solve it in a pupil's way?

[Guest]

You've probably drawn the diagram incorrectly. As it stands the answer would involve [tex]tan^{-1} 2[/tex] in some form.

If you additionally shaded the area that is on the bottom left (below the diagonal) then it is solvable by young children, as it just the area of the triangle minus the area of a circle.

Hope this helped,

R. Baber.

[Guest]

An answer is given at the below link
https://www.quora.com/What-is-the-area- ... haded-part
Please be aware they are using radians not degrees.
(Note that [tex]\arctan 0.5 = \tfrac{\pi}{2}-\tan^{-1} 2[/tex], so it does not disprove my claim.)

Hope this helped,

R. Baber.

[leesajohnson]

No idea how to solve it and I don't think that it is a question of primary school.

[Guest]

Most of the shaded areas can be calculated fairly easily.
The diagram shows 2 squares with 2 circles and some corners shaded....so there are 3.5 corners shaded plus a small bit more.
The area of a square is 10 x 10 = 100 sq units.
The area of a circle is Pi x 5^2 = 78.54 sq units
so corners shaded is 3.5(100 - 78.54)/4 = 18.7775 sq units.
The top RH corner is where there is a bit more that half a corner....a line from the centre of the circle at 45 deg. gives the middle of the

corner.....we need the area shaded from this line to the main diagonal line in the corner.
The main diagonal of the diagram makes an angle of arctan(0.5) = 26.565 degrees to horizontal so a line from (the intersection of the

main diagonal and the circle) to the centre of the circle makes an angle of 53.13 degrees to the horizontal. That give 8.13 degrees between this line and the 45 line.
The length of this small arc is Pi x 10 x 8.13 / 360 = 0.7095
The length of the 45 degree line outside the circle to the corner of the square will be (5 x sqrt2 - 5) = 2.0711
This area is small compared to rest of diagram so take it as a triangle of base 0.7095 and height 2.0711......area = 0.7347
So total shaded area is 18.7775 + 0.7347 = 19.5122 sq units.

[Guest]

In primary school finding areas is often introduced by drawing diagrams on graph or squared paper and counting the number of squares within the diagram.
Generally for simple diagrams. I imagine it would be quite difficult the get any reasonable accuracy counting squares on this diagram due to the number of curves, angles and narrow points etc.