Question

The right section of a prism is in the form of a regular hexagon whose apothem measures 6 cm. if the lateral area is 400 cm^2, what is the length of the lateral edge of the prism?  

 

e= ______cm

Answer 1

The apothem length a is related to the side length s which is the same as the radius of the hexagon. (½s)²+a²=s² so a=s√3/2=6, s=12/√3cm=6.9282cm approx. The lateral surface area is the area of 6 rectangles measuring sL sq cm each where L is the length of the prism. So 6sL = 400 and L = 400/6s = 200/(3s) = (200/3)(√3/12) = (50/3)/√3 = 9.6225cm approx.