To find the area of the shape provided in the updated image, let's go through the calculation again with the new dimensions.

Dimensions from the Image:

• The longer rectangle has dimensions $3 \, \text{m} \times 17.1 \, \text{cm}$.
• The shorter rectangle is $9.874 \, \text{m} \times 17.1 \, \text{cm}$.
• The quarter-circle has a radius of $17.1 \, \text{cm}$, which is $0.171 \, \text{m}$.

Convert all dimensions to meters:

• $17.1 \, \text{cm} = 0.171 \, \text{m}$
• The width of the rectangles is $0.171 \, \text{m}$.

Calculate the Areas:

1. Area of the longer rectangle: $A_1 = 3 \, \text{m} \times 0.171 \, \text{m} = 0.513 \, \text{m}^2$

2. Area of the shorter rectangle: $A_2 = 9.874 \, \text{m} \times 0.171 \, \text{m} = 1.687454 \, \text{m}^2$

3. Area of the quarter-circle: $A_3 = \frac{1}{4} \times \pi \times (0.171 \, \text{m})^2 = \frac{1}{4} \times \pi \times 0.029241 \, \text{m}^2 \approx 0.0229862 \, \text{m}^2$

Total Area:

$\text{Total Area} = A_1 + A_2 + A_3 = 0.513 \, \text{m}^2 + 1.687454 \, \text{m}^2 + 0.0229862 \, \text{m}^2 \approx 2.22344 \, \text{m}^2$

So, the total area of the shape is approximately 2.22344 m².

Would you like more details or have any questions?

Related Questions:

1. How would you find the perimeter of this shape?
2. What happens to the area if the radius of the quarter-circle is increased?
3. How does the area change if the length of the shorter rectangle is doubled?
4. What is the significance of converting all dimensions to the same unit before calculating the area?
5. How would you calculate the area if the quarter-circle segment was replaced with a half-circle?

Tip:

Always ensure that all dimensions are in the same unit when calculating areas to avoid errors and ensure accurate results.