Calculate Surface Area: 8×5×12 Cuboid Dimensions Problem

Surface Area with Cuboid Formula

Look at the cuboid below.

888555121212

What is the surface area of the cuboid?

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Determine the surface area of the box
00:04 Use the formula for calculating the surface area of a box
00:08 2 x (the sum of areas of all faces)
00:15 Substitute the appropriate values into the formula according to the given data and solve
00:30 Solve each multiplication separately
00:39 Sum up
00:46 Here is the solution to the problem

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

Look at the cuboid below.

888555121212

What is the surface area of the cuboid?

2

Step-by-step solution

Let's see what rectangles we have:

8*5

8*12

5*12

Let's review the formula for the surface area of a rectangular prism:

(length X width + length X height + width X height) * 2

Now let's substitute all this into the exercise:

(8*5+12*8+12*5)*2=
(40+96+60)*2=
196*2= 392

This is the solution!

3

Final Answer

392 cm²

Key Points to Remember

Essential concepts to master this topic
  • Formula: Surface area = 2(lw + lh + wh) for all six faces
  • Technique: Calculate 8×5 + 8×12 + 5×12 = 40 + 96 + 60
  • Check: Multiply by 2 and verify: 196 × 2 = 392 cm² ✓

Common Mistakes

Avoid these frequent errors
  • Forgetting to multiply by 2
    Don't calculate just one set of opposite faces = half the surface area! Students often find 8×5 + 8×12 + 5×12 = 196 and stop there. Always multiply by 2 because a cuboid has 6 faces (3 pairs of opposite faces).

Practice Quiz

Test your knowledge with interactive questions

A cuboid is shown below:

222333555

What is the surface area of the cuboid?

FAQ

Everything you need to know about this question

Why do I need to multiply by 2 at the end?

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A cuboid has 6 faces arranged in 3 pairs of opposite faces. Each pair has identical dimensions: two 8×5 faces, two 8×12 faces, and two 5×12 faces. So you calculate one of each pair, then multiply by 2!

What if I calculated each face separately?

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That works too! You'd get 8×5 + 8×5 + 8×12 + 8×12 + 5×12 + 5×12 = 392. The formula 2(lw + lh + wh) is just a shortcut to avoid writing each face twice.

How do I identify length, width, and height from the diagram?

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It doesn't matter which dimension you call length, width, or height! The formula works the same way. In this problem: 8, 5, and 12 can be assigned to l, w, h in any order.

What units should my final answer have?

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Surface area is always measured in square units (like cm², m², ft²). Since we're multiplying two lengths together for each face area, the result is length × length = length².

Can I use this formula for any rectangular prism?

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Yes! This formula 2(lw + lh + wh) works for any cuboid or rectangular prism, whether it's a box, room, or building block. Just substitute your three dimensions.

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