Calculate Base Area: Rectangular Prism with Volume 80 m³ and Height 4 m

Volume Formula with Base Area Calculation

The volume of the rectangular prism below is 80 m³.

The length of the lateral edge is 4 m.

What is the area of the base?

V=80V=80V=80444

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1

Understand the problem

The volume of the rectangular prism below is 80 m³.

The length of the lateral edge is 4 m.

What is the area of the base?

V=80V=80V=80444

2

Step-by-step solution

To solve this problem, we'll follow these steps:

  • Use the volume formula for the rectangular prism: V=Abase×h V = A_{\text{base}} \times h .
  • Rearrange the formula to solve for the base area: Abase=Vh A_{\text{base}} = \frac{V}{h} .
  • Substitute the given values into this rearranged formula.

Now, let's work through these steps:
Step 1: We know the volume V=80m3 V = 80 \, \text{m}^3 and the height h=4m h = 4 \, \text{m} .
Step 2: Using the formula Abase=Vh A_{\text{base}} = \frac{V}{h} , we substitute the given numbers:
Abase=804m2 A_{\text{base}} = \frac{80}{4} \, \text{m}^2 .
Step 3: Perform the division to find the area of the base:
Abase=20m2 A_{\text{base}} = 20 \, \text{m}^2 .

Therefore, the area of the base of the rectangular prism is 20m2 20 \, \text{m}^2 .

3

Final Answer

20

Key Points to Remember

Essential concepts to master this topic
  • Volume Formula: V = base area × height for any prism
  • Technique: Rearrange to A = V ÷ h: 80 ÷ 4 = 20 m²
  • Check: Verify: 20 m² × 4 m = 80 m³ matches given volume ✓

Common Mistakes

Avoid these frequent errors
  • Using wrong formula or confusing dimensions
    Don't use V = length × width × height and try to find individual dimensions = impossible with given information! You only have volume and height. Always use V = base area × height and solve for the missing base area directly.

Practice Quiz

Test your knowledge with interactive questions

A rectangular prism has a base measuring 5 units by 8 units.

The height of the prism is 12 units.

Calculate its volume.

121212888555

FAQ

Everything you need to know about this question

What exactly is the 'base area' of a rectangular prism?

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The base area is the area of the bottom face (or top face - they're identical). For a rectangular prism, it's length × width, but you don't need to find these individual dimensions!

Why don't I need to know the length and width separately?

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Because the problem asks for total base area, not individual dimensions. The formula A=Vh A = \frac{V}{h} gives you the area directly without needing length and width.

What does 'lateral edge' mean?

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The lateral edge is a vertical edge connecting the top and bottom faces. In this case, it's the height of the prism, which is 4 m.

How do I check if 20 m² is reasonable?

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Think about it: if the base area is 20 m² and height is 4 m, then 20 × 4 = 80 m³, which matches the given volume perfectly!

Can the base area ever be larger than the volume?

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Yes! If the height is less than 1 meter, the base area will be numerically larger than the volume. For example: V = 10 m³, h = 0.5 m gives base area = 20 m².

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