Question

O prisma triunghiulara regulata ABCA'B'C' are latura bazei de 5 cm si inaltimea de 15 cm.
a).Aflati volumul prismei
b).Aflati aria totala a prismei

Answer 1

Răspuns:

Explicație pas cu pas:

Presupun ca este o prisma dreapta.

a) V = Ab x h = l^2 rad3  /  4   x   h =

25rad3  /  4     x   15 = 15x25rad3  /  4 = 375rad3  /  4 = 93,75rad3 cm^3 ≅ 162,24 cm^3

b) At = 2Ab + Al = l^2 rad3  /  2 + 3(5x15) =

25rad3  /  2  + 3x75 =

25rad3 / 2 + 225 =

25(rad3 / 2 + 9) =

25(rad3 + 18) / 2 ≅ 12,5 * 19,73 ≅ 246,65 cm^2

Answer 2

$\it a)\ \mathcal{V} =\mathcal{A}_b\cdot h\\ \\ \mathcal{A}_b=\dfrac{\ell^2\sqrt3}{4}= \dfrac{5^2\sqrt3}{4}=\dfrac{25\sqrt3}{4}\ cm^2\\ \\ \\ \mathcal{V}=\dfrac{25\sqrt3}{4}\cdot15=\dfrac{375\sqrt3}{4}cm^3$

$\it \mathcal{A}_{\ell}=3\cdot\mathcal{A}_{ABB'A'}=3\cdot5\cdot15\ =225\ cm^2\\ \\ \mathcal{A}_t=\mathcal{A}_{\ell} +2\cdot\mathcal{A}_b=225+2\cdot\dfrac{25\sqrt3}{4}=225+\dfrac{25\sqrt3}{2}=\dfrac{450+25\sqrt3}{2}\ cm^2$