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Math Help

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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

#1
+27229
+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
+27229
+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
#2
+201
+5

Thank you.

mathcalc  Jun 2, 2015