3D Pythagoras

With 3D shapes sometimes you need to use Pythagoras more than once to find a particular length.

Cuboids

There’s a formula in cuboids for finding the length of the longest diagonal.3d pythagoras in a cuboidOther Shapes

Example: Find the height x for the below pyramid.3d pythagoras pyramidFirst find the length AC

 

ac2 = ab2 + bc2

ac2 = 144 + 144 = 288

ac = 16.97056…

So ay is half this.

ay = 8.48528…

So now you have another right angled triangle you can work out:

av2 = ay2 + x2

so:

x2 = av2 – ay2 = 400 – (8.48528…)2 = 400 – 72 = 328

So x is the square root of 328

So x = 18.11 (2 d.p.)