I have thin matchsticks each of thickness 1 mm. The length of each matchstick is ‘L ’ mm. There are a few matchsticks kept side by side on a table such that the heads of all matchsticks are in one line and the tail ends of all matchsticks are together in another different line and the lengths of the matchsticks are parallel. The number of matchsticks kept is ‘B’. What is the area of the plane formed by the matchsticks (in ${m m}^{2}$ )?

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Solution

This problem has been given to make you understand how a 2-D planar area can be constructed and its magnitude obtained.

The below diagram represents how the matchsticks have been kept together. They are kept side by side along the width.

To obtain the 2-D area I am placing thin matchsticks of given length side by side. This means that a 2-D area can be obtained by stacking together lengths of unit thickness/breadth. This thickness/breadth is the $2^{n d}$ dimension. The length is the first dimension. This means that an area consists of 2 measurable dimensions.

In our example total area of plane of matchsticks = Length each of matchstick × number of matchsticks × Breadth of one matchstick

= L × B × 1 = LB ${m m}^{2}$

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