Find the lateral surface and total surface area of a cuboid of length 80 cm, breadth 40 cm and height 20 cm.

To find the lateral surface area and the total surface area of a cuboid, we can use specific formulas that relate to its dimensions. In this case, we have a cuboid with a length of 80 cm, a breadth of 40 cm, and a height of 20 cm. Let’s break down the calculations step by step.

Lateral Surface Area Calculation

The lateral surface area of a cuboid refers to the area of the sides, excluding the top and bottom faces. The formula for the lateral surface area (LSA) is:

• LSA = 2h(l + b)

Where:

• h = height
• l = length
• b = breadth

Substituting the values:

• h = 20 cm
• l = 80 cm
• b = 40 cm

Now, plug these values into the formula:

• LSA = 2 × 20 × (80 + 40)
• LSA = 2 × 20 × 120
• LSA = 2 × 2400
• LSA = 4800 cm²

Total Surface Area Calculation

The total surface area (TSA) of a cuboid includes all six faces. The formula for the total surface area is:

• TSA = 2(lb + bh + hl)

Using the same dimensions:

• l = 80 cm
• b = 40 cm
• h = 20 cm

Now, substitute these values into the TSA formula:

• TSA = 2 × (80 × 40 + 40 × 20 + 20 × 80)
• TSA = 2 × (3200 + 800 + 1600)
• TSA = 2 × 5600
• TSA = 11200 cm²

Summary of Results

To summarize, for the cuboid with the given dimensions:

• Lateral Surface Area: 4800 cm²
• Total Surface Area: 11200 cm²

These calculations help in understanding the properties of the cuboid and can be useful in various practical applications, such as packaging, construction, and design. If you have any further questions or need clarification on any part of the process, feel free to ask!