To find the area of the shape provided in the image, we need to break it down into simpler parts:

1. Identify the components:

   • The shape consists of two rectangles and a quarter-circle segment.

2. Dimensions from the image:

   • The longer rectangle has dimensions $300 \, \text{cm} \times 17.1 \, \text{cm}$.
   • The shorter rectangle is $98.74 \, \text{cm} \times 17.1 \, \text{cm}$.
   • The quarter-circle has a radius of $17.1 \, \text{cm}$, which corresponds to the width of the rectangles.

3. Calculate the areas:

   • Area of the longer rectangle: $A_1 = 300 \, \text{cm} \times 17.1 \, \text{cm} = 5130 \, \text{cm}^2$

   • Area of the shorter rectangle: $A_2 = 98.74 \, \text{cm} \times 17.1 \, \text{cm} = 1687.454 \, \text{cm}^2$

   • Area of the quarter-circle: $A_3 = \frac{1}{4} \times \pi \times (17.1 \, \text{cm})^2 = \frac{1}{4} \times \pi \times 292.41 \, \text{cm}^2 \approx 229.862 \, \text{cm}^2$

4. Total area: $\text{Total Area} = A_1 + A_2 + A_3 = 5130 \, \text{cm}^2 + 1687.454 \, \text{cm}^2 + 229.862 \, \text{cm}^2 \approx 7047.316 \, \text{cm}^2$

So, the total area of the shape is approximately 7047.316 cm².

Would you like more details or have any questions?

Related Questions:

1. What is the perimeter of the entire shape?
2. How would the area change if the quarter-circle were a half-circle?
3. Can the same shape be constructed with different dimensions to get a similar area?
4. How does the area change if the radius of the quarter-circle is doubled?
5. What if the shape is scaled down by half, what would be the new area?

Tip:

When dealing with composite shapes, breaking them into smaller, recognizable shapes simplifies the process of calculating areas and perimeters.