Find the area of the shaded region:
\(\frac{642}{7} \text{ cm}^2\)
\(\dfrac{642}{7}\ \text{cm}^2\) is correct.
The area of a shaded region is found by taking the area of the complete outer figure and subtracting the areas of the unshaded parts shown in the diagram.
Rectangular or triangular parts use \(l \times b\) or \(\dfrac{1}{2} \times b \times h\), and circular parts use \(\pi r^2\) (or a fraction of it for a semicircle or quadrant) with \(\pi = \dfrac{22}{7}\).
Because \(\pi = \dfrac{22}{7}\) is used, the result has denominator 7; with the dimensions in the figure, the shaded area comes to \(\dfrac{642}{7}\ \text{cm}^2\).
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