Use the Pythagorean theorem to find the lengths of diagonals in solid figures such as rectangular prisms and cubes.
Diagonal of a Rectangular Prism
For a rectangular prism with length a, width b, and height c, the diagonal d is:
d = √(a² + b² + c²)
📘 Example ①
Find the diagonal of a rectangular prism with length 2cm, width 3cm, and height 6cm.
Answer:d = √(2² + 3² + 6²) = √(4 + 9 + 36) = √49 = 7cm
Find the diagonal of a rectangular prism with length 2cm, width 3cm, and height 6cm.
Answer:d = √(2² + 3² + 6²) = √(4 + 9 + 36) = √49 = 7cm
💡 Key Point
- Diagonal = √(a² + b² + c²)
- Calculate in stages: find the diagonal of the base, then combine it with the height
Practice Problem
- Find the diagonal of a cube with side length 4cm (you may leave the answer as √3).
Answer and Explanation
- Answer:4√3 cm. √(4²+4²+4²)=√48=4√3.