Paint the Pyramids Purple

3D Trigonometry/Pythagoras

slanted edge

The great pyramid at Giza in Egypt has a square base and four triangular faces.

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.

slanted edge

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.

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.

146 m

162·6 m

Pythagoras’ theoreml

47754·76

2

l 218·528..

l

219 m162·6

146

2 2 2146 162·6l

(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

219 m

230 m 347362 186·375..

h 186·4 m

h

115 m

Pythagoras’ theorem2 2 2219 115h

2 2 2219 115h

Area of triangle base × height

12

(230)(186·4)

12

21436 m2

2006 Paper 2 Q5 (b)

slanted edge

(ii) Calculate, correct to two significant numbers, the total area of the four triangular faces of the pyramid (assuming they are smooth flat surfaces)

219 m

347362 186·375..

h 186·4 m

h

115 m

Pythagoras’ theorem2 2 2219 115h

2 2 2219 115h

Total area 21436 4

85744 m2 86000 m2

2006 Paper 2 Q5 (b)