Let’s solve this step-by-step based on the information visible in the image.

The Figure Description

The figure consists of two connected rectangles. One rectangle is taller, while the other is wider. The relevant dimensions are:

• Tall rectangle: Height = 114 ft, Width = 41 ft
• Wide rectangle: Height = 44 ft, Width = 59 ft

Let’s break the questions down:

(a) What is the area of the figure?

The total area will be the sum of the areas of both rectangles.

• Area of the tall rectangle = Height × Width = 114 ft × 41 ft = 4674 square feet
• Area of the wide rectangle = Height × Width = 44 ft × 59 ft = 2596 square feet

Now, sum both areas:
$4674 + 2596 = 7270 \, \text{square feet}$

So, the correct area is: $7270 \, \text{square feet}$

(b) What is the perimeter of the figure?

Since the two rectangles are connected, we need to account for shared sides to avoid counting them twice.

• Full height of the shape: $114 \, \text{ft} + (59 - 41) \, \text{ft} = 114 + 18 = 132 \, \text{ft}$
• Total width of the shape: $59 \, \text{ft}$

Now, the perimeter can be found by adding all the outside edges: $\text{Perimeter} = 2(\text{Height} + \text{Width}) = 2(132 + 59) = 2(191) = 382 \, \text{feet}$

So, the correct perimeter is: $382 \, \text{feet}$

(c) How much greater is the area of the figure than its perimeter?

To find this difference: $7270 \, \text{(area)} - 382 \, \text{(perimeter)} = 6888$

So, the correct difference is: $6888$

Summary of Answers:

• (a): Area = 7270 square feet
• (b): Perimeter = 382 feet
• (c): Difference between area and perimeter = 6888

Let me know if you need further clarification or if any step is unclear! Here are some related questions for further practice:

1. How do you handle overlapping regions when calculating the area of complex shapes?
2. What is the formula for the perimeter of other polygons like triangles or pentagons?
3. How can you break irregular shapes into simpler components for area calculation?
4. If the units were in meters instead of feet, how would the area and perimeter change?
5. How can knowing the area and perimeter help in real-world applications like fencing or flooring?

Tip: Double-check shared boundaries when dealing with composite shapes, as these can affect both area and perimeter!