Write the formula for LSA of cuboid and explain each term in it.

To find the lateral surface area (LSA) of a cuboid, we use the formula:

Formula for Lateral Surface Area of a Cuboid

The formula is given by:

LSA = 2h(l + w)

Breaking Down the Terms

Let’s take a closer look at each term in this formula:

• h: This represents the height of the cuboid. It is the vertical distance from the base to the top face of the cuboid.
• l: This is the length of the cuboid. It refers to the longer side of the base rectangle.
• w: This stands for the width of the cuboid. It is the shorter side of the base rectangle.

Understanding the Calculation

The lateral surface area of a cuboid is essentially the area of the four vertical faces that connect the top and bottom faces. To visualize this, imagine wrapping a box with paper, but only covering the sides and leaving the top and bottom open. The formula accounts for the area of these four sides.

When we break down the formula:

• The term (l + w) calculates the combined length of the two different dimensions of the base rectangle. This sum gives us the perimeter of the base rectangle when multiplied by the height.
• Multiplying by 2 accounts for the fact that there are two faces for each dimension (one on each side). Thus, we are effectively calculating the area of the two pairs of opposite sides.
• Finally, multiplying by h gives us the total area of the vertical sides, as each side's area is determined by its height and its respective base length or width.

Example Calculation

Let’s say we have a cuboid with a height of 5 units, a length of 10 units, and a width of 4 units. Plugging these values into the formula:

LSA = 2 * 5 * (10 + 4)

Calculating inside the parentheses first:

10 + 4 = 14

Now substituting back into the formula:

LSA = 2 * 5 * 14 = 140 square units

This means the lateral surface area of the cuboid is 140 square units. This area represents the total surface area of the four vertical sides of the cuboid.

Real-World Application

Understanding the lateral surface area is useful in various practical scenarios, such as determining how much paint is needed to cover the sides of a box or how much wrapping paper is required for a gift. By mastering this concept, you can apply it to everyday situations effectively.