To find the area of the shape in the diagram, we can break it down into simpler parts and subtract the area of the inner cutout from the area of the large outer rectangle.

Step 1: Calculate the area of the large outer rectangle

The dimensions of the large outer rectangle are:

• Width = 72 ft
• Height = 30 ft

The area of the rectangle is given by: $\text{Area of large rectangle} = \text{width} \times \text{height} = 72 \, \text{ft} \times 30 \, \text{ft} = 2160 \, \text{ft}^2$

Step 2: Calculate the area of the inner cutout

The cutout is a smaller rectangle in the middle of the larger one with the following dimensions:

• Width = 32 ft
• Height = 12 ft

The area of the cutout is: $\text{Area of cutout} = \text{width} \times \text{height} = 32 \, \text{ft} \times 12 \, \text{ft} = 384 \, \text{ft}^2$

Step 3: Subtract the area of the cutout from the area of the large rectangle

Now, subtract the area of the inner cutout from the area of the large rectangle: $\text{Total area} = \text{Area of large rectangle} - \text{Area of cutout} = 2160 \, \text{ft}^2 - 384 \, \text{ft}^2 = 1776 \, \text{ft}^2$

Thus, the total area of the shape is 1776 square feet.

Would you like more details or have any questions?

Here are 5 related questions:

1. How would you find the perimeter of this shape?
2. What would the area be if the dimensions of the cutout were different?
3. Can you explain why we subtracted the inner area?
4. How would the approach change if there were more cutouts?
5. Could this method apply to 3D shapes for finding volume?

Tip: When calculating areas of complex shapes, breaking them down into simpler shapes (like rectangles, triangles, etc.) makes the process much easier.