By splitting the shape into a semi-circle and rectangle, we can see that we have a semi-circle with a diameter of 14 cm and a rectangle with dimensions of 28 cm by 15 cm. To find the area of the entire shape, we can add the areas of the two shapes up.
We can find the area of the semi-circle using the formula [tex] \frac{\pi r^2}{2} [/tex], where [tex] r [/tex] is the radius of the semi-circle. In this case, the area would be:
[tex] \dfrac{\pi (14)^2}{2} = \dfrac{196\pi}{2} = 98 \pi \,\,\textrm{cm}^2 [/tex]
The formula for the area of a rectangle is [tex] lw [/tex], where [tex] l [/tex] is the length of the rectangle and [tex] w [/tex] is the width. In this case, the area would be:
[tex] (28)(15) = 420 \,\,\textrm{cm}^2 [/tex]
Thus, the area of the total shape is:
[tex] 98 \pi \,\,\textrm{cm}^2+ 420 \,\,\textrm{cm}^2 \approx \boxed{727.88 \,\,\textrm{cm}^2} [/tex]
