1. Paint the Pyramids Purple
3D Trigonometry/Pythagoras

2. How much will it cost to paint the whole pyramid?
The great pyramid at Giza in Egypt has a square base and four triangular faces.
slanted edge
How much will it cost to paint the whole pyramid?
Your report should include
Assumptions that you have made.
Research findings
Clear maths, diagrams and explanations.
Conclusions/Improvements.
Sommets 5
Faces 5
BSommets 5

3. The top of the pyramid is directly above the centre of the base.
The great pyramid at Giza in Egypt has a square base and four triangular faces.
The base of the pyramid is of side 230 metres and the pyramid is 146 metres high.
slanted edge
The top of the pyramid is directly above the centre of the base.
(i) Calculate the length of one of the slanted edges, correct to the
nearest metre.
Pythagoras’ theorem l
146 m
Sommets 5
Faces 5
BSommets 5
= ·76 l 2
146
l = 218·528..
162·6
162·6 m
= 219 m
Sommets 5
Faces 5
BSommets 5

4. (ii) Calculate, correct to
two significant numbers, the total area of the four triangular faces of the pyramid (assuming they are smooth flat surfaces)
slanted edge
Pythagoras’ theorem
219 m h h 2 =
= 186·375..
= 186·4 m
115 m
230 m
Sommets 5
Faces 5
BSommets 5
Area of triangle = base × height 1 2
= (230)(186·4) 1 2
= m2
2006 Paper 2 Q5 (b)
Sommets 5
Faces 5
BSommets 5

5. (ii) Calculate, correct to
two significant numbers, the total area of the four triangular faces of the pyramid (assuming they are smooth flat surfaces)
slanted edge
Pythagoras’ theorem
219 m h h 2 =
= 186·375..
= 186·4 m
115 m
Sommets 5
Faces 5
BSommets 5
Total area
=  4
= m2
= m2
2006 Paper 2 Q5 (b)
Sommets 5
Faces 5
BSommets 5