1)
d = l√3 = 8√3 => l = 8 cm
V = l³ = (8cm)³ = 512 cm³
2)
d = √(L² + l² + h²)
= √(36 + 108 + 81)
= √225
= 15 cm
3)
Al = 240 = Pb×h
240cm² = Pb×8cm
Pb = 240cm²/8cm = 30 cm
Pb = 30cm = 3×l => l = 30/3 = 10 cm
V = Ab×h
= l²√3×h/4
= 100cm×8cm×√3/4
= 800√3cm²/4
= 200√3 cm²
4)
d = √(l² + h²)
= √(100 + 200)
= √300
= √3×10²
= 10√3 cm
5)
BD' = √(AB²+BC²+AA'²) = √(128 + 64 + 64) = √256 = 16 cm
duc AE ⊥ BD' (AE = d(A;BD'))
ΔABD' = dreptunghic =>
=> AB×AD' = AE×BD'
AE = AD'×AB/BD'
= 8√2×8√2/16 = √2×√2 = 2 cm
6)
AD' ; AC ; CD' = diagonale in patrat =>
AD' = AC = CD' => ΔACD'= echilateral
inaltimea intr-un echilateral este data de formula
h = l√3/2, unde l = latura triunghiului ACD' si in cazul nostru este egala cu diagonala fetelor patratului adica AD' ; AC ; CD'
AC = AB√2 = 12√2 cm
h = 12√2×√3/2 = 6√6 cm
d(C ; AD') = h = 6√6 cm
