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 $SA = 2(lw + lh + wh)$.
Answer for screen readers
The formula for the surface area of a rectangular solid is given by $$ SA = 2(lw + lh + wh) $$.
Steps to Solve
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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.
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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.
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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
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Add the Products Add the three products calculated in the previous step: $$ lw + lh + wh $$
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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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