To calculate the area of this composite shape, let's break it down into simpler parts. The figure is composed of a rectangle and a quarter circle.

Step-by-Step Solution:

1. Identify Dimensions of the Rectangle:

   • The rectangle has a height and width, both of which are labeled as 30 cm.

   $\text{Area of Rectangle} = \text{Length} \times \text{Width} = 30 \, \text{cm} \times 30 \, \text{cm} = 900 \, \text{cm}^2$

2. Identify the Quarter Circle:

   • The quarter circle has a radius equal to the side length of the rectangle, which is 30 cm.
   • To find the area of the quarter circle, we use the formula for the area of a circle and then take a quarter of it:

   $\text{Area of Quarter Circle} = \frac{1}{4} \times \pi \times r^2 = \frac{1}{4} \times \pi \times (30)^2$

   • Plugging in the value of $\pi \approx 3.14159$:

   $\text{Area of Quarter Circle} = \frac{1}{4} \times 3.14159 \times 900 \approx 706.8575 \, \text{cm}^2$

3. Combine the Areas:

   • Now, add the area of the rectangle and the area of the quarter circle to get the total area.

   $\text{Total Area} = 900 + 706.8575 \approx 1606.8575 \, \text{cm}^2$

   Rounding to one decimal place, we get:

   $\text{Total Area} \approx 1606.9 \, \text{cm}^2$

Conclusion:

The closest answer to this calculation is: 1,606.5 cm².

Would you like a more detailed breakdown or have any questions?

Follow-up Questions:

1. How do we calculate the area of different circle fractions like half-circles or quarter circles?
2. What would the total area be if the radius of the quarter circle was doubled?
3. How does changing the side length of the rectangle affect the area of the entire shape?
4. Can we use this approach for composite shapes that involve other figures like triangles?
5. How would the area calculation change if this were a three-dimensional shape?

Tip:

In composite area problems, breaking the shape down into known geometric figures simplifies the calculation.