S=A+B+C, where S total area and A, B and C are areas of shadows figures at side a, b and c.
A = (pi/2)*[(a/2)^2-(a1/2)^2+(a2/2)^2] B = (pi/2)*[(b/2)^2-(b1/2)^2+(b2/2)^2] C = (pi/2)*[(c/2)^2-(c1/2)^2+(c2/2)^2]
h1^2 + c1^2 = h3^2 + a2^2 h1^2 + c2^2 = h2^2 + b1^2 h2^2 + b2^2 = h3^2 + a1^2, by Pythagoras T. where h1, h2 and h3 are distance of point P to side c, b and a.
This is not attempted yet? It is not that hard!
ReplyDeleteAnswer is D.
ReplyDeleteS=A+B+C, where S total area and A, B and C are areas of shadows figures at side a, b and c.
A = (pi/2)*[(a/2)^2-(a1/2)^2+(a2/2)^2]
B = (pi/2)*[(b/2)^2-(b1/2)^2+(b2/2)^2]
C = (pi/2)*[(c/2)^2-(c1/2)^2+(c2/2)^2]
h1^2 + c1^2 = h3^2 + a2^2
h1^2 + c2^2 = h2^2 + b1^2
h2^2 + b2^2 = h3^2 + a1^2, by Pythagoras T. where h1, h2 and h3 are distance of point P to side c, b and a.
-c1^2+c2^2-b1^2+b2^2-a1^2+a2^2 = 0
a=b=c=1
S=3*(pi/2)*1/4 = 3*pi/8.
MIGUE.
S = 3 identical semi-circles (radius=1/2) - A(ABC) - A(ABC) <-- ses Fox 213 (http://8foxes.blogspot.com/2009/12/fox-213.html)
ReplyDeleteS = 3 identical semi-circles (radius=1/2)
S = 3*(pi * (1/2)^2)/2
S = 3 * pi * 1/4 * 2
S = 3pi/8