Pythagoras In 3D Shapes'

1
Pythagoras In 3D Shapes.
AG 2 L 2 B 2 H 2
2
Finding The Length Of A Space Diagonal.
Look at the cuboid below
It is our task to calculate the length of the
space diagonal AG which runs through the space
inside the cuboid.

• Start by considering the triangle ABC.

(2) Calculate the length of AC.
AC 30.5cm
or
? 928
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Now look at the cuboid again.
(3) Now consider triangle ACG.
(4) Calculate the length of AG.
AG 34.4cm
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What Goes In The Box ?
Calculate the lengths of the space diagonals in
the cuboids below
Answer
13m
Answer
38.7cm
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Pythagoras Pyramids.
Consider the rectangular based pyramid below
28cm is the slant height EC.
Our task is to find the vertical height EF as
shown.
(1) Consider the triangle ABC.
(2) Calculate the length of AC.
AC 13.9cm
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Now look at the pyramid again
(3) Now consider triangle EFC.
(4) Calculate the length of EF.
EF 27.1cm
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What Goes In The Box ? 2
Calculate the length of the required line below
Answer
7.8m
Answer
9.4m