Given a right prism ABC.A’B’C’. It bases is a right angle at B and AB = 8cm; AC = 10 cm. Assume that A’B = 17 cm, the lateral area of this prism is..

0 bình luận về “Given a right prism ABC.A’B’C’. It bases is a right angle at B and AB = 8cm; AC = 10 cm. Assume that A’B = 17 cm, the lateral area of this prism is..”

1. Because $∆ABC$ is right at $B$

   So $BC^2+BA^2=AC^2$ (Pythagorean theorem)

   Or $BC^2+8^2=10^2$

   Thus $BC=6(cm)$

   So the perimeter of the base is: $AB+BC+AC=8+6+10=24(cm)$

   B is the right angle so B’ is the right angle too and AB=A’B’=8cm so ∆A’B’B is a right triangle

   So $A’B’^2+B’B^2=A’B^2$

   $<=>8^2+BB’^2=17^2$

   $<=>BB’^2=225$

   $<=>BB’=15cm$

   Or the height of the prism is 15cm

   Thus the lateral area of the prism is:

   Height. Perimeter of the base/2=BB’.24/2=15.24/2=180cm^2

   Bình luận