How to find the surface area of a rectangular solid?

Understand the Problem

The question is asking how to calculate the surface area of a rectangular solid, which involves using the formula for surface area that includes the dimensions of the solid (length, width, and height).

Answer

The surface area of a rectangular solid is calculated using the formula $SA = 2(lw + lh + wh)$.

Steps to Solve

Identify the Dimensions Determine the length ($l$), width ($w$), and height ($h$) of the rectangular solid. You will need these values to calculate the surface area.
Use the Surface Area Formula The surface area ($SA$) of a rectangular solid can be calculated using the formula: $$ SA = 2(lw + lh + wh) $$ This formula accounts for all the rectangular faces of the solid.
Calculate Each Component Calculate the products of the dimensions that appear in the formula:

$lw$: multiply length by width
$lh$: multiply length by height
$wh$: multiply width by height

Add the Products Add the three products calculated in the previous step: $$ lw + lh + wh $$
Multiply by 2 Finally, multiply the result from the addition by 2 to get the total surface area: $$ SA = 2(lw + lh + wh) $$

The formula for the surface area of a rectangular solid is given by $$ SA = 2(lw + lh + wh) $$.

More Information

The surface area of a rectangular solid is essential in various fields such as construction, manufacturing, and packaging. Understanding this concept helps in calculations related to material costs and space utilization.

Tips

Forgetting to multiply by 2 at the end of the calculation. Always ensure to follow through the formula completely.
Confusing the order of width, length, and height. Be careful to label the dimensions correctly.

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