# 03 Area enclosed by pairs of overlapping quarter circles

**Example 03**

The shaded regions in the figure below are areas bounded by two circular arcs. The arcs have center at the corners of the square and radii equal to the length of the sides. Calculate the area of the shaded region.

**Solution 03**

Area CEB is equal to area of the square OAEF minus area of the quarter circle OABCF minus four times the area of CED.

$A_{CED} = 8.68 \, \text{ cm}^2$ → *See how it was found*

Area of CEB

$A_{CEB} = A_{square} - A_{OABCF} - 4A_{CED}$

$A_{CEB} = 20^2 - \frac{1}{4} \pi (20^2) - 4(8.68)$

$A_{CEB} = 51.12 \, \text{ cm}^2$

Required Area

$A_{required} = 4A_{CEB} = 4(51.12)$

$A_{required} = 204.48 \, \text{ cm}^2$ *answer*

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