Find the z-scores that separate the middle % of the distribution from the area in the tails of the standard normal distribution.

(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