Answer to Question #148926 in Geometry for solid mensuration

Question

4. The lateral edge of a square prism is 20 cm long and it is inclined at an angle of 60 degrees with the base. If the volume of the prism is 1,200 cm3, determine the base edge.

Answer 1

Consider a regular square pyramid

Let $a=$ the base edge, $h=$ the altitude, and $l=$ the lateral edge.

The volume $V$ of the of a regular square prism is

$$V=a^2h$$

Then

$$a=\sqrt{\dfrac{V}{h}}$$

From the right triangle

$$h=l\sin60\degree$$

$$a=\sqrt{\dfrac{1200}{20(\dfrac{\sqrt{3}}{2})}}=2\sqrt{10\sqrt{3}}(cm)$$

$a=2\sqrt{10\sqrt{3}}\ cm$