Math Problem Statement

Find the surface are of the figure below

Find the surface area of the figure below.

Solution

The figure you've provided appears to be a rectangular prism (or cuboid) with dimensions:

  • Length (l) = 15 meters
  • Width (w) = 6 meters
  • Height (h) = 4 meters

To find the surface area of a rectangular prism, you can use the formula:

Surface Area=2lw+2lh+2wh\text{Surface Area} = 2lw + 2lh + 2wh

Substituting the values:

Surface Area=2(15×6)+2(15×4)+2(6×4)\text{Surface Area} = 2(15 \times 6) + 2(15 \times 4) + 2(6 \times 4) =2(90)+2(60)+2(24)= 2(90) + 2(60) + 2(24) =180+120+48= 180 + 120 + 48 =348square meters= 348 \, \text{square meters}

So, the surface area of the rectangular prism is 348 square meters.

Would you like further details or have any questions?

Here are 5 related questions to extend your understanding:

  1. How would the surface area change if the height was doubled?
  2. What is the volume of this rectangular prism?
  3. How does surface area differ between a cube and a rectangular prism?
  4. What is the surface area of a cylinder with the same height and diameter as the base of this prism?
  5. How can surface area calculations be applied in real-world scenarios like construction?

Tip: When calculating surface area, always ensure you account for all sides of the 3D shape to avoid missing any surface!

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Math Problem Analysis

Mathematical Concepts

Geometry
Surface Area Calculation
Rectangular Prisms

Formulas

Surface Area of a Rectangular Prism = 2lw + 2lh + 2wh

Theorems

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Suitable Grade Level

Grades 7-9