The problem of mathematical projection

The projection of (1) and △ABC on O is MH line.

The projection of △A 1B 1C 1 on O is a straight line NK.

The projection of quadrilateral AA 1B 1B on O is line segment MN.

The projection of quadrilateral AA 1C 1C and BB 1C 1C on O is a rectangle mnkh(CD∑MH, CD⊥AB).

(2) Surface area

△ABC area =△A 1B 1C 1 area ab * CD/2 = (√ 3/3) CD * CD = (√ 3/3) MH * MH = 4 √ 3/3.

[AB=2√3/3CD]

Quadrilateral aa1b1b = ab * Mn = 2 √ 3/3.

CD*MN=2√3/3

MH*HK=8√3/3

The quadrilateral aa1c1c = bb1c1c = AC * cc1= hk * 2 √ 3/3mh = 8 √ 3/3.

So the surface area =32√3/3.

Note: √3 is the root number 3.