Each leg of the right triangle has length 6 cm. Find the area of the green square.
Dividing this into 9 segments, we find that the square takes up 4 segments. 4/9 * the area of the triangle = 4/9*18=
8
+128475 Let A = (0,6) B = (0,0) and C = (6,0)
AC = 6sqrt (2)
Triangle ADE is similar to triangle ABC
Call the side of the square, S = DE
So
AD/ DE = AB/BC
AD /S = 6/6
AD = S
And triangle CFG is similar to triangle CBA
So
FG/ CF = BA/ CB
S / CF = 6/6
CF = S
So
AD + DF + FC = 6sqrt (2)
S + S + S = 6sqrt (2)
3S = 6sqrt (2)
S = 2sqrt (2) = sqrt(8) cm
Area of square = 8 cm^2
