Question

oblicz pole powierzchni calkowitej szescianu o krawedzi a (wsk. P=6a^2)

a)

Answer 1

a)

a = 2√3-1

P = 6a²

P = 6(2√3-1)² = 6[(2√3)²-2·2√3·1+1²] = 6(12-4√3+1) = 6(13-4√3) = 78-24√3

 

b)

a = √6+√2

P = 6a²

P = 6[(√6)²+2·√6·√2+(√2)²] = 6(6+2√12+2) = 6(8+2√(4·3) = 6(8+2·√4·√3) = 6(8+4√3) = 48+24√3

 

 

(a+b)² = a²+2ab+b²

(a-b)²  = a²-2ab+b²