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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
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3+0 Answers

 #1
avatar+5589 
+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 cm2

 

yellow area = (1/2)(π*42) - 8

yellow area = (1/2)(16π) - 8

yellow area = 8π - 8 cm2

hectictar  Apr 28, 2017
 #2
avatar+428 
+1

i dont think i understand

waffles  Apr 29, 2017
 #3
avatar+5589 
+1

I can try to explain my answer more thoroughly smiley

 

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 sq. cm.

 

yellow section = (1/2) * 16π - 8

yellow section = 8π - 8   sq. cm.

hectictar  Apr 30, 2017
edited by hectictar  Apr 30, 2017

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