Cuboid Dimension Challenge: Is Base Identification Necessary for 5x8x2 Surface Calculation?

Given an cuboid whose dimensions are 5,8,2

Indicate whether it is true or false:

To calculate the surface of the cuboid it is not necessary to know which are the sides of the base and which is the height.

To solve this problem, we begin by calculating the surface area of the cuboid using its dimensions. The surface area formula for a cuboid is:

$\text{Surface Area} = 2(lw + lh + wh)$

Substituting the dimensions 5, 8, and 2 into the formula, we calculate:

$\text{Surface Area} = 2((5 \times 8) + (5 \times 2) + (8 \times 2))$

$\text{Surface Area} = 2(40 + 10 + 16)$

$\text{Surface Area} = 2(66)$

$\text{Surface Area} = 132$

Regardless of the assignment of dimensions as length, width, or height (due to the commutative nature of multiplication), the computed surface area remains the same at 132 square units.

Thus, it is indeed true that determining which dimensions are the base or height is unnecessary for calculating a cuboid's surface area. The computation yields consistent results irrespective of the assignment.

Therefore, the statement is true.