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The figure is made up of four identical squares of side length 12 inches. A Quadrant is drawn inside each square. Find the total area of shaded parts of figure. Use 3.14 as approximation of Pi.

 

mathcalc  Jun 1, 2015

Best Answer 

 #1
avatar+26969 
+10

Imagine the outer squares are hinged at the bottom (where they meet their adjacent squares).  Rotate them about the hinge until they are below the other two squares, so a large square is formed.  

 

The arc's then form a complete circle of radius 12 inches.  

Inscribed in this circle is a square of side 12*√2 inches.

 

The shaded area is just the difference between the circle area and the square area.  i.e.

 

 

shaded area = pi*144 - 144*2 square inches

.

Alan  Jun 1, 2015
 #1
avatar+26969 
+10
Best Answer

Imagine the outer squares are hinged at the bottom (where they meet their adjacent squares).  Rotate them about the hinge until they are below the other two squares, so a large square is formed.  

 

The arc's then form a complete circle of radius 12 inches.  

Inscribed in this circle is a square of side 12*√2 inches.

 

The shaded area is just the difference between the circle area and the square area.  i.e.

 

 

shaded area = pi*144 - 144*2 square inches

.

Alan  Jun 1, 2015
 #2
avatar+201 
+5

Thank you.

mathcalc  Jun 2, 2015

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