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Rectangular Prism — Definition, Formula & Examples

A rectangular prism is a three-dimensional shape with six faces that are all rectangles. It has 8 vertices, 12 edges, and every pair of opposite faces is identical.

A rectangular prism (also called a cuboid or right rectangular parallelepiped) is a polyhedron bounded by three pairs of congruent, parallel rectangular faces that meet at right angles along 12 edges. It is fully determined by three independent length measurements: length, width, and height.

Key Formula

V = l \times w \times h$$ $$SA = 2(lw + lh + wh)
Where:
  • VV = Volume of the rectangular prism
  • SASA = Surface area of the rectangular prism
  • ll = Length of the prism
  • ww = Width of the prism
  • hh = Height of the prism

How It Works

To work with a rectangular prism, you need its three dimensions: length (ll), width (ww), and height (hh). The volume tells you how much space the prism occupies — multiply all three dimensions together. The surface area tells you the total area covering the outside — add up the areas of all six rectangular faces. Since opposite faces match, you only need to compute three distinct face areas and double the sum. Everyday objects like shoeboxes, bricks, and shipping containers are all rectangular prisms.

Worked Example

Problem: A rectangular prism has a length of 8 cm, a width of 5 cm, and a height of 3 cm. Find its volume and surface area.
Step 1: Find the volume by multiplying length, width, and height.
V=8×5×3=120 cm3V = 8 \times 5 \times 3 = 120 \text{ cm}^3
Step 2: Compute the area of each distinct pair of faces.
lw=8×5=40,lh=8×3=24,wh=5×3=15lw = 8 \times 5 = 40, \quad lh = 8 \times 3 = 24, \quad wh = 5 \times 3 = 15
Step 3: Add those three areas and double the result to get the total surface area.
SA=2(40+24+15)=2(79)=158 cm2SA = 2(40 + 24 + 15) = 2(79) = 158 \text{ cm}^2
Answer: The volume is 120 cm³ and the surface area is 158 cm².

Another Example

Problem: A fish tank shaped like a rectangular prism is 60 cm long, 30 cm wide, and 40 cm tall. How many liters of water can it hold? (1 liter = 1,000 cm³)
Step 1: Calculate the volume in cubic centimeters.
V=60×30×40=72,000 cm3V = 60 \times 30 \times 40 = 72{,}000 \text{ cm}^3
Step 2: Convert cubic centimeters to liters by dividing by 1,000.
72,000÷1,000=72 liters72{,}000 \div 1{,}000 = 72 \text{ liters}
Answer: The fish tank holds 72 liters of water.

Why It Matters

Rectangular prisms appear constantly in middle-school geometry and standardized tests when you study surface area and volume. Beyond the classroom, architects calculate room volumes for heating and cooling, and shipping companies figure out how many boxes fit inside a cargo container — all using rectangular prism measurements. Mastering this shape builds the foundation for working with more complex 3D solids like cylinders and pyramids.

Common Mistakes

Mistake: Confusing volume and surface area formulas — for example, multiplying all three dimensions and calling it surface area.
Correction: Volume uses one multiplication (l×w×hl \times w \times h), while surface area requires computing three different face areas and doubling their sum: 2(lw+lh+wh)2(lw + lh + wh).
Mistake: Forgetting to double when calculating surface area, giving only half the total.
Correction: Each rectangular face has an identical match on the opposite side. After adding lw+lh+whlw + lh + wh, you must multiply by 2 to account for all six faces.

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