Math Problem Statement

What is the surface area of the rectangular prism based on the provided net?

Solution

The problem asks for the surface area of the rectangular prism whose net is shown in the diagram. To solve, we calculate the total surface area of all six rectangular faces.

Dimensions of the rectangular prism:

  • The prism consists of:
    • 2 rectangular faces measuring 8cm×10cm8 \, \text{cm} \times 10 \, \text{cm},
    • 2 rectangular faces measuring 8cm×5cm8 \, \text{cm} \times 5 \, \text{cm},
    • 2 rectangular faces measuring 5cm×10cm5 \, \text{cm} \times 10 \, \text{cm}.

Surface Area Calculation:

  1. Calculate the area of each pair of rectangles:

    • 2×(8×10)=2×80=160cm22 \times (8 \times 10) = 2 \times 80 = 160 \, \text{cm}^2,
    • 2×(8×5)=2×40=80cm22 \times (8 \times 5) = 2 \times 40 = 80 \, \text{cm}^2,
    • 2×(5×10)=2×50=100cm22 \times (5 \times 10) = 2 \times 50 = 100 \, \text{cm}^2.
  2. Add the areas of all six rectangles: 160+80+100=340cm2.160 + 80 + 100 = 340 \, \text{cm}^2.

Final Answer:

The surface area of the rectangular prism is: 340cm2.\boxed{340 \, \text{cm}^2}.

Would you like a detailed explanation of any of these steps or have additional questions?


Here are 5 related questions to explore:

  1. How do you calculate the surface area of a cube?
  2. What happens to the surface area if you double all the dimensions of a prism?
  3. Can you calculate the volume of this prism with the given dimensions?
  4. How does the net of a triangular prism differ from that of a rectangular prism?
  5. What is the relationship between the dimensions and surface area for any rectangular prism?

Tip: Always double-check the dimensions of the net to ensure you’ve identified all the faces of the 3D figure!

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Math Problem Analysis

Mathematical Concepts

Geometry
Surface Area
Nets of 3D Shapes

Formulas

Surface Area = 2(lw + lh + wh)

Theorems

Surface area of a rectangular prism

Suitable Grade Level

Grade 6-8