Question

The sides of bases of a pentagonal prism are 4cm, 5cm, 7cm, 9cm and 10cm. The height of the prism is 6cm. Find the total length of its edges (in cm).
$
  {\text{A}}{\text{. 100}} \\
  {\text{B}}{\text{. 90}} \\
  {\text{C}}{\text{. 110}} \\
  {\text{D}}{\text{. 120}} \\
$

Answer 1

Hint – In order to find the total edge length, we calculate the sum of all the sides in the pentagonal prism, its sides which represent the height included. We construct a suitable figure to count the sides easily.
Complete step-by-step answer::

A pentagon has 5 sides on each of its upper and lower face. And it has a total of 5 sides which are equivalent to its height, from the figure.
It has 15 edges in total.
Given data, sides are of lengths 4cm, 5cm, 7cm, 9cm and 10cm. And it has a height of 6cm.
So the total edge length of this pentagonal prism
= 2 (4 + 5 + 7 + 9 + 10) + 5 (6)
=2 (35) + 30
=70 + 30
=100 cm.
So the total edge length of the pentagonal prism = 100cm.
Hence Option A is the correct answer.
Note – In order to solve this type of question the key is to understand the definition of a pentagonal prism. A pentagonal prism is a prism that has two pentagonal bases like top and bottom and five rectangular sides. It is a type of heptahedron with 7 faces, 10 vertices and 15 edges. Its base shape is a pentagon and its side shape is a rectangle.