# 04 Four overlapping semi-circles inside a square

**Example 04**

The figure shown below consists of arcs of four semi-circles with centers at the midpoints of the sides of a square. The square measures 20 cm by 20 cm. Find the area bounded by these circular arcs shaded in the figure shown.

**Solution 04**

$A_1 = \frac{1}{4} \pi (10^2) - \frac{1}{2}(10)(10)$

$A_1 = 28.54 \, \text{ cm}^2$

Required Area

$A_{required} = 8A_1 = 8(28.54)$

$A_{required} = 228.32 \, \text{ cm}^2$ *answer*

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