Answer to Question #148230 in Trigonometry for yui

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,

____________________ 2) What is the base edge in cm?

____________________ 3) What is the lateral area of the prism in cm2?

_____________________ 4) What is the total area of the square prism in cm2?

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