A circle is placed in a square with a side length of 18 mm, as shown below. Find the area of the shaded region. Use the value 3.14 for it, and do not round your answer. Be sure to include the correct unit in your answer.

geometry: triangles

solvers

lessons

answers archive

call the larger triangle abc

then the smaller triangle cde is similar to abc (all angles are equal, aaa).  

ab is the side that is 36, and we wish to find de, the side corresponding to ab

area_cde = area_abc - area_cde --> area_abc / area_cde = 2

let x=length of de

ratio of areas = (ratio of sides)^2

+2+=+%2836%2fx%29%5e2+

+2+=+1296%2fx%5e2+

++x%5e2+=+1296%2f2+=+648+

25.45584

80x^8−68x^6+16^5−20x^4−4x^3+8x^2

hope i'm right lol