Surface Area Calculation: Find Total Area of 5 dm × 4 cm × 0.3 dm Box

To solve this problem, we'll follow these steps:

• Step 1: Convert all dimensions to the same unit.

• Step 2: Apply the surface area formula for a cuboid.

• Step 3: Calculate the total surface area.

Now, let's work through each step:

Step 1: Convert all dimensions to the same unit. For consistency, we will convert everything to decimeters (dm):

• Width = 5 dm (already in dm)

• Height = 4 cm. To convert cm to dm, divide by 10: $4 \, \text{cm} = 0.4 \, \text{dm}$.

• Depth = 0.3 dm (already in dm)

Step 2: Apply the surface area formula for a cuboid:

The surface area $A$ is given by:

$A = 2lw + 2lh + 2wh$

Where:

• $l = 0.3 \, \text{dm}$ (depth)

• $w = 5 \, \text{dm}$ (width)

• $h = 0.4 \, \text{dm}$ (height converted to dm)

Substitute these values into the formula:

$A = 2(0.3)(5) + 2(0.3)(0.4) + 2(5)(0.4)$

Step 3: Calculate the surface area:

$A = 2(1.5) + 2(0.12) + 2(2)$

$A = 3 + 0.24 + 4$

$A = 7.24 \, \text{dm}^2$

Note that the question requires the surface area in different units.

Thus, 7.24 dm² is 72.4 cm²

Therefore, the solution to the problem is 72.4 cm².