The Application of the Pythagorean Theorem to an Orthohedron or Cuboid

🏆Practice use of the pythagorean theorem in the orthohedron

The orthohedron or cuboid is a rectangular prism, a three-dimensional figure, that is, it has length, width, and height (or depth). In addition, the angles between the different planes are right angles, which allows us to make use of the Pythagorean theorem to calculate the length of different sections of the orthohedron.

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Test yourself on use of the pythagorean theorem in the orthohedron!


Which of the options has a marked diagonal equal to the diagonal described in the given drawing?


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We will illustrate this with an example.

Given an orthohedron as represented in the diagram.

The dimensions of the box are 6 6 , 8 8 and 10 10 .

We are asked to calculate the dimensions of the diagonal of the lower base of the box.

We will look at the diagram and see that the base of the box is, in fact, a rectangle whose edges measure 6 6 and 8 8 . These edges also serve as legs with a right angle between them.

Therefore, we will use the Pythagorean theorem and calculate the hypotenuse which, in fact, is the required diagonal.

According to the Pythagorean theorem we will obtain:

X=10 X=10

That is, the diagonal measures 10 10 .

If you are interested in learning more about other triangle topics, you can go to one of the following articles:

  • The Pythagorean Theorem
  • Acute Triangle
  • Obtuse Triangle
  • Scalene Triangle
  • Equilateral Triangle
  • Isosceles Triangle
  • The edges of a triangle
  • Area of a right triangle
  • Height of a triangle
  • How to calculate the perimeter of a triangle?
  • Congruent triangles:
  • Criterion of congruence: Side, Angle, Side
  • Congruence Criterion: Angle, Side, Angle
  • Congruence criterion: Side, Side, Side
  • Area of a right triangle

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