It's been a while since I saw a good puzzle on the forum. This one is adapted from something I saw on line.
Find the shaded area. Make the usual assumptions of right angles and circular arc. I worked it using only geometry.
1893.4sq whatever units; with some assumptions.
1893.7 also w assumptions and a significant amount of rounding.
(confession: I did have to look up middle ordinate formula)
1893.18
Used law of sines and A^2 + B^2 = C^2
We agree on the answer. Here's my method:
Do we assume the arc is tangent at the corners?
My assumption was to make the curve tangent as it intersects the NW and SE corners of the square so a PI at the northeast corner and tangent lengths of 100.
It appears to be necessary to assume tangency.
Back to my old calculation days for it. So many of the numbers are derived without formulas or calculators. The west side of the area is a triangle 50x50/2. From there it's rectangles and triangles.
The one number you need a formula for (beyond A times B) is the mid ordinate distance 29.2893, use it and the rest of the calculations are a ratio. 29.2893/70.7107 gives you everything you need to figure out the area. That gives you a distance of 41.4213 from the NE corner of the square to the northeast corner of the area figure. From there its easy, just multiplication and division.
DUH!!!!!!!!!!!!!
It just dawned on me that the mid ordinate is the easy number.
The radius of the circle is clearly 100 so the mid ordinate is 100-70.7107.
I don't do this stuff enough anymore. So simple, it's a thought puzzle not a calculation puzzle.
