Answer to Question #138134 in Geometry for Nirvana

Question

The lateral edge of a square prism is 30 cm long and it is inclined at an
angle of 70 degrees with the base. If the volume of the prism is 1,500 cm3,
1. what is the base edge?
2. What is the lateral area of the prism?
3. What is the total area of the square prism?

Answer 1

1. $V=B²h$

B=Base edge

h=height

$h=\sin(70\degree)×30=28.2 cm$

$B=\sqrt{V \over h}=\sqrt{1500\over 28.2}=7.3cm$

2. Lateral area of the prism is $L.A.=4Bh=4×7.3×28.2=823.44 cm²$

3. Total area of = ph+2A

p=perimeter of the base

h=height of the prism

A=Area of the base

p = 4×7.3 = 29.2cm

h = 28.2cm

A = 7.3 × 7.3 = 53.29cm²

T.A. = (29.2 ×28.2) + 53.29

= 823.44 + 53.29 = 876.73cm²