DIMENSI TIGA - Panjang diagonal sisi dan diagonal ruang Balok

Introduction

This tutorial will guide you through the process of calculating the length of the diagonal edges and the space diagonal of a rectangular prism (balok) in three dimensions. Understanding these concepts is essential for solving problems in geometry and real-world applications such as architecture and engineering.

Step 1: Understanding the Dimensions of a Rectangular Prism

To calculate the diagonals, first ensure you know the dimensions of the rectangular prism:

• Length (l)
• Width (w)
• Height (h)

These measurements are crucial for the calculations that follow.

Step 2: Calculating the Diagonal of a Face

Each face of the rectangular prism is a rectangle, and you can find the diagonal of any face using the Pythagorean theorem.

1. Identify the dimensions of the face you're calculating the diagonal for.

   • For the face with dimensions length and width, use:
   • Diagonal of face (d_f):

   d_f = √(l² + w²)
   

2. Calculate the diagonal using the identified dimensions.

Step 3: Calculating the Space Diagonal

The space diagonal is the longest diagonal that goes from one corner of the prism to the opposite corner. It can also be calculated using the Pythagorean theorem, but in three dimensions.

1. Use the formula for the space diagonal (d_s):

   d_s = √(l² + w² + h²)
   

2. Substitute the length, width, and height into the formula.

Step 4: Practical Example

To solidify your understanding, let’s do a practical example.

• Assume a rectangular prism has:
  • Length (l) = 3 units
  • Width (w) = 4 units
  • Height (h) = 5 units

1. Calculate the diagonal of a face (length and width):

   d_f = √(3² + 4²) = √(9 + 16) = √25 = 5 units
   

2. Calculate the space diagonal:

   d_s = √(3² + 4² + 5²) = √(9 + 16 + 25) = √50 ≈ 7.07 units
   

Conclusion

In this tutorial, you learned how to determine the lengths of the diagonal edges and the space diagonal of a rectangular prism. Remember to always start with the correct dimensions and apply the Pythagorean theorem appropriately for both 2D (face diagonals) and 3D (space diagonal) calculations. Next, consider exploring how these calculations apply in real-world scenarios like designing furniture or constructing buildings.