+647 The circle is inscribed in a square with sides 8 cm. What is the area of the shaded part in square centimeters? Express your answer in terms of pi.
+9479 yellow area = (1/2)(area of circle) - area of middle triangle
area of middle triangle = (1/2) (base) (height)
area of middle triangle = ( 1/2 ) ( 8 ) ( [8/2]/2 )
area of middle triangle = ( 1/2 ) ( 8 ) ( 2 ) = 8 cm2
yellow area = (1/2)(π*42) - 8
yellow area = (1/2)(16π) - 8
yellow area = 8π - 8 cm2
+9479 I can try to explain my answer more thoroughly 
Here I have shaded in the middle triangle and labeled points A, B, and C.
The yellow section is half of the area of the circle MINUS the area of the gray triangle.
area of the circle = π * radius2
area of the circle = π * (4)2
area of the circle = 16π sq. cm.
area of the gray triangle = (1/2) * base * height
the base = 8 and the height = AO
Point O cuts line CB in half..OB = (1/2) * CB
Point A cuts line OB in half..AO = (1/2) * OB
We know line CB = 8....so OB = (1/2) * 8 = 4... and.. AO = (1/2) * 4 = 2
So, the height = 2, and the base = 8.
area of the gray triangle = (1/2) * 8 * 2
area of the gray triangle = 8 sq. cm.
The yellow section is half of 16π MINUS 8 sq. cm.
yellow section = (1/2) * 16π - 8
yellow section = 8π - 8 sq. cm.
