Question

Prisma triunghiulara reg. are Aria toatala=72radical3 si Aria laterala=54radical3
a) lungimea laturii bazei
b) inaltimea(h)
c) masura unghiului formar de (C'AB) SI (ABC)

Answer 1

a)
notam cu a latura bazei
h=√[a²-(a/2)²]=√3a²/4=a√3/2
Abazei= (72√3-54√3) /2=18√3/2=9√3
Abazei=(axa√3/2)/2=a²√3/4 = 9√3
a²=36
a=6
b)
h=a√3/2=6√3/2=3√3
c)  A laterala=54√3
    P=6x3=18
H = 54√3/18=3 √3
tg α = H/h=3√3/3√3=1
α=45⁰