QUICK WILL GIVE 100 POINTS !! The last remaining of the Seven Wonders of the ancient world, the great pyramids of Giza are perhaps the most famous and discussed structures in history. Many questions remain about the construction of these massive monuments, and theories abound as to the actual methods used. Using your knowledge about the shape of the Pyramids of Giza to answer the following questions. To attain maximum credit please include any websites used for references. Your reflection should include complete sentences and at least 4 paragraphs. (1) What shape is the base of the pyramids in Giza? What are some other shapes the base of pyramids can be? (20 pts) (2) How tall is the tallest pyramid in Giza? Would it be possible to build a bigger pyramid today? Why or Why not? (30 pts) (3) What would be the dimensions of a pyramid you had to build (make sure you include (a)height, (b) length, (c) base shape, (d) surface area, and (e) slope)? (50 pts)

(1) Square; triangle or pentagon

(2)  Originally 146.6 m, now 139 m

(3) (a) h = 150 m; (b) l = 240 m; (c) base = square;

    (d) lateral area = 92 205 m²; (e) slope = 5/4

Step-by-step explanation:

(1) Base

The pyramids at Giza have square bases. Those are the most common, but the bases can have any number of shapes, e.g., triangles  or pentagons.

(2) Size

The Great Pyramid was originally 146.6 m tall with a base that was 230.4 m on each side. It is now only 139 m tall, because the limestone casings  have fallen away.

It would be possible to build a bigger pyramid today, because modern machinery can easily handle the massive stones.

(3) A larger pyramid

A larger modern pyramid might be 150 m tall and have a square base 240 m on each side.

(a) Height = 150 m

(b) Length = 240 m

(c) Base shape = square

(d) Surface Area

The square pyramid has four triangular faces.

(i) Side height

We can use Pythagoras' Theorem to calculate the side height s of the pyramid:

s² = 120² + 150² = 36 900 m²

s = √36900 = 192.1 m

(ii) Lateral area

The pyramid has four triangular faces.

Each triangle has a base of 240 m and a height of 192.1 m.

The formula for the area of a triangle is  

A = ½bh

So. the area of the four triangles is

A = 4 × ½bh = 2bh = 2 × 240 m × 192.1 m = 92 205 m²

(e) Slope of pyramid

slope = Δy/Δx = 150/120 = 5/4

so a parallelogram is just like a square base times height. multiply 40 and 39 to get 1560 inches.

a triangle is base times height divided by two. so multiply 7.9 and 5 and then divide it by 2 to get 19.75inches.

the kite can be split into two separate triangles and added together to get the total area. 30 x 4 /2 which equals 60. make sure to double it for the two triangles making 120.