Math Problem Statement

What is the surface area of the cuboid below? (Dimensions: 12m x 7m x 4m)

Solution

The given image shows a cuboid with dimensions:

  • Length: 12 meters
  • Width: 7 meters
  • Height: 4 meters

To find the surface area AA of a cuboid, we use the formula:

A=2(lw+lh+wh)A = 2(lw + lh + wh)

where:

  • ll is the length,
  • ww is the width,
  • hh is the height.

Substituting the given values:

A=2(12×7+12×4+7×4)A = 2(12 \times 7 + 12 \times 4 + 7 \times 4)

Now, I'll calculate that.The surface area of the cuboid is 320m2320 \, \text{m}^2.

Would you like further details on the calculation or have any other questions?

Here are some related questions for further exploration:

  1. What is the volume of this cuboid?
  2. How would the surface area change if the height doubled?
  3. What is the difference between surface area and lateral surface area for this cuboid?
  4. How can you find the diagonal of this cuboid?
  5. How does surface area scale with the size of the cuboid's dimensions?

Tip: Always check units when solving geometry problems to ensure the final answer makes sense.

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Math Problem Analysis

Mathematical Concepts

Geometry
Surface Area
Cuboids

Formulas

Surface area of a cuboid: A = 2(lw + lh + wh)

Theorems

Basic properties of three-dimensional shapes

Suitable Grade Level

Grades 5-7