Math Problem Statement

Translate the sentence into an equation or formula.

The surface area SA of a rectangular prism is 2 times the sum of the width (w) times height (h), and length ( 𝓁 ) times width, and length times height.

Solution

The sentence can be translated into the following formula for the surface area (SA) of a rectangular prism:

SA=2(wh+w+h)SA = 2(w \cdot h + \ell \cdot w + \ell \cdot h)

Where:

  • SASA is the surface area
  • ww is the width
  • hh is the height
  • \ell is the length

This formula accounts for the fact that a rectangular prism has six faces, with three pairs of opposite faces having equal areas.

Would you like more details or have any questions?

Here are 5 related questions:

  1. How do you derive the surface area of a rectangular prism step by step?
  2. How does the surface area formula change for a cube?
  3. What is the surface area if w=3w = 3, h=4h = 4, and =5\ell = 5?
  4. How does the formula for surface area differ from the formula for volume?
  5. Can you express the surface area formula for a cylinder?

Tip: When calculating surface area, always remember to multiply the areas of each pair of faces by 2 since each pair occurs twice in the shape.

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Math Problem Analysis

Mathematical Concepts

Geometry
Surface Area
Rectangular Prism

Formulas

SA = 2(w * h + ℓ * w + ℓ * h)

Theorems

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Suitable Grade Level

Grades 6-8