Pythagoras In 3D Shapes. F 28cm 12cm 16cm AB C D E G H AG 2 = L 2 + B 2 + H 2.

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Presentation transcript:

Pythagoras In 3D Shapes. F 28cm 12cm 16cm AB C D E G H AG 2 = L 2 + B 2 + H 2

F 28cm 12cm 16cm AB C D E G H 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. (1)Start by considering the triangle ABC. (2) Calculate the length of AC. A C AC = 30.5cmor  928

Now look at the cuboid again. F 28cm 12cm 16cm AB C D E G H 30.5cm (3) Now consider triangle ACG. (4) Calculate the length of AG. A G AG = 34.4cm

What Goes In The Box ? Calculate the lengths of the space diagonals in the cuboids below: (1) 4m 3m 12m (2) 26cm 17cm 23cm Answer: 13m 38.7cm

Pythagoras & Pyramids. Consider the rectangular based pyramid below: A B CD E 12cm 7cm 28cm 28cm is the slant height EC. Our task is to find the vertical height EF as shown. F (1) Consider the triangle ABC. (2) Calculate the length of AC. AC = 13.9cm 12 7 A C B

Now look at the pyramid again: A B CD E 12cm 7cm 28cm 13.9cm F (3) Now consider triangle EFC. (4) Calculate the length of EF. 28cm 6.95cm E FC EF = 27.1cm Half of AC.

What Goes In The Box ? 2 Calculate the length of the required line below: 6.3m 3.2m 7m A B CD E (2) F Length EC. Answer: 9.4m 7.8m A B CD E (1) 14.6 m 9.8 m 12.9 m Length EF. F