Find the area and the number of bricks needed to construct the pyramid

Question

The pyramid of Giza in Egypt has a base of 100 meters and a lateral edge of 139.3 meters. The average volume of each brick used to construct it is 1.6 m^3. Originally it was covered by a glistening layer of white tile.

a.) What is the area of the tile needed to cover the pyramids surface?

b.) How many bricks were needed to construct the pyramid? (assuming it was solid)

 

Answer 1

Sam,

For the tiles, we look at the lateral surface area of the pyramid. The lateral surface can be described as four congruent isosceles triangles, each with a base of 100 and sides of 139.3. The area of a triangle is 1/2*base*height. But first we must find the height.

 

If we bisect the angle at the peak with an altitude line, we create a right triangle with a base of 50 and a hypotenuse of 139.3. So we can find the length of the altitude (height of the triangle) with Pythagorean theorem:

 

h = √(139.3² - 50²) = 130 meters

 

So each triangle has an area of:

 

A = 1/2(100)(130) = 6500 m²

 

The total area of tile is 4 * 6500 = 26000 m²

 

For the number of bricks to build a solid pyramid, we'll just use the volume of the pyramid divided by the volume of a brick.  The volume of a pyramid can be expressed as:  V = 1/3(area of the base)(height)

 

The area of the base is easy:  100 * 100 = 10000 m²

 

The height is a little trickier. Try to picture a right triangle formed by the height through the center of the pyramid, a line from the center of the base to the midpoint of an edge, and a hypotenuse from the midpoint of the edge to the peak.

 

The base is 1/2(100) = 50

 

The hypotenuse is the height of the surface triangle we found in part a)  =  130 m

 

Again, we use Pythagorean theorem to find  h = √(130² - 50²) = 120 m

 

V = 1/3(10000)(120) = 400,000 m³

 

So the number of bricks is = 400,000 / 1.6 = 250,000 bricks