1. Identify the Given Information

• The square has a side length of \( s = 6 \) cm.
• Two semi-circles are drawn inside the square. Their diameters are the left and bottom sides of the square.
• The radius of each semi-circle is half the side of the square: $ r = \frac{6}{2} = 3 \text{ cm} $

2. Analyze the Shaded Region

By observing the image, we can see that the shaded region consists of two identical semi-circles, but the area where they overlap (the "leaf" shape in the bottom-left corner) is unshaded (white). Thus, the total shaded area is the sum of the areas of the two semi-circles minus twice the area of their overlap.

Let's divide the \( 6 \times 6 \) square into four smaller \( 3 \times 3 \) squares. The intersection of the two semi-circles happens entirely within the bottom-left \( 3 \times 3 \) square.

3. Mathematical Calculation

• Area of one semi-circle: $ A_{\text{semi}} = \frac{1}{2} \pi r^2 = \frac{1}{2} \pi (3)^2 = 4.5\pi \text{ cm}^2 $
• Area of the overlap (Leaf shape): The overlap is formed by two quarter-circles inside a \( 3 \times 3 \) square. The area of one quarter-circle is \( A_{\text{qc}} = \frac{1}{4} \pi (3)^2 = 2.25\pi \). The area of the overlap is: $ A_{\text{overlap}} = 2 \times A_{\text{qc}} - \text{Area of } 3\times3 \text{ square} $ $ A_{\text{overlap}} = 2(2.25\pi) - 3^2 = 4.5\pi - 9 $
• Total Shaded Area: According to the visual, the shaded area is the union of the two semi-circles, excluding the overlap twice (since it's white in both): $ \text{Area}_{\text{shaded}} = A_{\text{semi 1}} + A_{\text{semi 2}} - 2 \times A_{\text{overlap}} $ Substituting the values: $ \text{Area}_{\text{shaded}} = 4.5\pi + 4.5\pi - 2(4.5\pi - 9) $ $ \text{Area}_{\text{shaded}} = 9\pi - (9\pi - 18) $ $ \text{Area}_{\text{shaded}} = 18 \text{ cm}^2 $