Answer to Question #138883 in Geometry for coco

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 is1,500cm3,
1.what is the base edge?
2.What is the lateral area of the prism?
3.What is the total areas of the square prism?

Answer 1

Volume of the prism:$V=h*S_{base}$

$h-height$

$h=\sin(70\degree)*30=28.2 cm$

$S_{base}=V/h=1500/28.2=53.2cm^2$

The base of the prism is a square, so base edge is $a=\sqrt{S_{base}}=7.3 cm$

Lateral area of the prism is $S_{lateral}=a*lateral edge=7.3*30=219 cm^2$

Total areas of the square prism is $S_{total}=2*S_{base}+4*S_{lateral}=2*53.2+4*219=982.4 cm^2$