Geometry » Long diagonal
What is a long diagonal (cross-section)?
On the right you can see a cuboid. In this cuboid there is a cross-section drawn in with yellow. Because one of the long diagonals (AG) is in this cross-section, you may call this a long diagonal cross-section. Such a cross-section is always rectangular.
In this cuboid together with ACGE, long diagonal cross-section are also:
BDHF, BCHE, ADGF, DCFE en ABGH.
In total 6 possible long diagonal cross-sections.
As said in these cross-section you can draw the long diagonal. In this drawing AG. A long diagonal is a line between two vertices and travels through the figure. BH, CE and DF are also long diagonals of this cuboid.
How do you calculate the length of a long diagonal?
We again look at the cuboid above.
Let's assume we need to calculate AG.
Follow this algorithm with 4 steps:
|1.||Find a long diagonal cross-section with the long diagonal in it.|
We are in luck, a usable long diagonal cross-section is already drawn.
We could also use ABGH.
|2.||Make a sketch of this cross-section and include the letters and given measurements.|
|3.||Find out which measurements you need before you can calculate the long diagonal.|
In this case we do not know AC, although we do need it. We can use Pythagoras to calculate AC.
|4.||Calculate the length of the long diagonal.|
You have to use Pythagoras again:
AG = ≈ 7.48 cm
How can you calculate another length within a cuboid?
What if you need to calculate the distance between C and the middle of side AE.
Check Pythagoras' theorem.