Question

How many square yards are present in \[1800\] square feet?

Answer 1

Hint:We use some conversions and calculations of different units to solve this problem. We mainly use unitary methods to solve this problem. We will generalize the definition of area and unitary method while solving this problem.

Complete step by step answer:
In mathematics, length is measured in meters, centimeters, inches, feet, kilometers and so on. An area is measured in square meters, square feet, square kilometers and many others.Generally, area is defined as multiple lengths. It is a 2-Dimensional measurement. So, it is a product of two dimensions, both are lengths. Consider a line of length \[4\,cm\].

Now, if you keep on adding some other lines on this line vertically, up to a length of \[3cm\], then it looks like this,

So, covers an area of \[4cm \times 3cm = 12c{m^2}\]
This is the way we calculate area.
Now, let us know some relations between quantities.
\[1{\text{ foot }} = 12{\text{ inches}}\]
And \[1{\text{ meter }} = 100{\text{ centimeters}}\]
These are some relations between quantities related to length.

Now, let us see some relations between quantities related to area.
\[1{\text{ sq}}{\text{.meter }} = 10000{\text{ sq}}{\text{.centimeters}}{\text{.}}\]
And \[1{\text{ sq}}{\text{.yard }} = 9{\text{ sq}}{\text{.foot}}\]
So, generally, an area whose length is 3 feet and breadth is 3 feet, is known as a yard.

Generally, this area shown above is called a yard.
So, now, from unitary method,
\[1{\text{ sq}}{\text{.yard }} = 9{\text{ sq}}{\text{.foot}}\]
\[\Rightarrow x{\text{ sq}}{\text{.yard }} = 1800{\text{ sq}}{\text{.foot}}\]
So, cross multiply the terms in these two equations, we get,
\[9 \times x = 1 \times 1800\]
\[ \therefore x = \dfrac{{1800}}{9} = 200\]

So, we can conclude that there are 200 square yards in 1800 square feet.

Note:In a unitary method, we will first find the value of one unit and then calculate the value of the number of units required to us. Area is always measured in square units.While volume is a 3-Dimensional measurement and its units are in cubic units.Remember the relations and conversions which will be helpful for you to solve further problems.