To solve this problem, let's address each part one by one:

Part (i) Finding the Area

The shape can be divided into three distinct rectangles:

1. Top rectangle with dimensions $10 \, \text{in} \times 4 \, \text{in}$.
2. Middle rectangle with dimensions $3 \, \text{in} \times 2 \, \text{in}$.
3. Bottom rectangle with dimensions $6 \, \text{in} \times 2 \, \text{in}$.

Let's calculate the area of each rectangle separately, then add them up for the total area.

Calculation:

1. Top Rectangle: $10 \times 4 = 40 \, \text{square inches}$
2. Middle Rectangle: $3 \times 2 = 6 \, \text{square inches}$
3. Bottom Rectangle: $6 \times 2 = 12 \, \text{square inches}$

Total Area = $40 + 6 + 12 = 58 \, \text{square inches}$

Part (ii) Finding the Perimeter

To find the perimeter, we add up the lengths of all outer sides of the shape.

Starting from the top-left and moving clockwise around the shape:

• Top side: $10 \, \text{in}$
• Right side 1: $2 \, \text{in}$
• Right side 2: $2 \, \text{in}$
• Right side 3: $2 \, \text{in}$
• Bottom side: $6 \, \text{in}$
• Left side 1: $2 \, \text{in}$
• Left side 2: $3 \, \text{in}$
• Left side 3: $4 \, \text{in}$

Calculation:

Perimeter = $10 + 2 + 2 + 2 + 6 + 2 + 3 + 4 = 31 \, \text{inches}$

Final Answers:

1. Area = $58 \, \text{square inches}$
2. Perimeter = $31 \, \text{inches}$

Would you like additional explanations on any part of the solution?

Here are five related questions to consider:

1. How would you calculate the area if one side measurement was missing?
2. What changes in the perimeter calculation if a side is lengthened?
3. Can this shape be divided in a different way to find the area?
4. How would you find the diagonal length of the top rectangle?
5. What is the difference between perimeter and area in practical applications?

Tip: When working with composite shapes, divide them into simpler shapes to make calculations easier.