A shape is formed by a rectangle and a semicircle. The rectangle has a length of 57 cm and a width of 16 cm. The semicircle's diameter is the same as the rectangle's width. Calculate the total area of

The length of the rectangle is $57 \text{ cm}$ and the width is $16 \text{ cm}$.

$$\text{Area}_{\text{rectangle}} = \text{length} \times \text{width}$$ $$\text{Area}_{\text{rectangle}} = 57 \text{ cm} \times 16 \text{ cm}$$ $$\text{Area}_{\text{rectangle}} = 912 \text{ cm}^2$$

The diameter of the semicircle is $16 \text{ cm}$, so the radius is $r = \frac{16}{2} = 8 \text{ cm}$.
We use $\pi = 3.142$.

$$\text{Area}_{\text{semicircle}} = \frac{1}{2} \pi r^2$$ $$\text{Area}_{\text{semicircle}} = \frac{1}{2} \times 3.142 \times (8 \text{ cm})^2$$ $$\text{Area}_{\text{semicircle}} = \frac{1}{2} \times 3.142 \times 64 \text{ cm}^2$$ $$\text{Area}_{\text{semicircle}} = 3.142 \times 32 \text{ cm}^2$$ $$\text{Area}_{\text{semicircle}} = 100.544 \text{ cm}^2$$

$$\text{Total Area} = \text{Area}_{\text{rectangle}} + \text{Area}_{\text{semicircle}}$$ $$\text{Total Area} = 912 \text{ cm}^2 + 100.544 \text{ cm}^2$$ $$\text{Total Area} = 1012.544 \text{ cm}^2$$

$$\text{Total Area} \approx 1012.5 \text{ cm}^2$$

The area of the shape is $\text{1012.5 cm}^2$.