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.

waffles
Apr 28, 2017

#1**+3 **

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 cm^{2}

yellow area = (1/2)(π*4^{2}) - 8

yellow area = (1/2)(16π) - 8

yellow area = 8π - 8 cm^{2}

hectictar
Apr 28, 2017

#3**+1 **

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 * radius^{2}

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.

hectictar
Apr 30, 2017