In 3D problems, find a right-angled triangle inside the solid. For the diagonal of a cuboid, first find the diagonal of the base with Pythagoras, then use it with the height in a second right-angled triangle.
The space diagonal of a cuboid with sides a, b and c is √(a² + b² + c²). To find the angle between a diagonal and the base, use the vertical edge as the opposite side and the base diagonal as the adjacent side, then tan⁻¹.
Worked example
A cuboid is 3 cm by 4 cm by 12 cm. Find the length of its space diagonal.
- Base diagonal: √(3² + 4²) = 5.
- Space diagonal: √(5² + 12²) = √169.
Answer:13 cm
Key words
- space diagonal
- a diagonal through the inside of a solid
- plane
- a flat surface
- projection
- the shadow of a line on the base
Practise this
New questions every time.
Common Core-referenced: HSG-SRT.C.8