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# The side of a square field is $89$ m. By how many square meters does its area fall, short of a hectare?

Last updated date: 24th Jul 2024
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Hint: In this problem we are going to find the area of square and then find the remaining area to fall, short of a hectare by subtracting the area from hectare. The field is square in shape, a square is a closed, two-dimensional shape with four equal sides. The hectare is a non-SI metric unit of area equal to a square with $100$ metre sides, or $10,000 {m^2}$, that is, $1$ hectare $= 10000{m^2}$, and is primarily used in the measurement of land.

Complete step-by-step solution:
In this problem,
We are given that the side of a square field is $89m$, that is, side $s = 89m$.

We know that all the sides of a square are equal.
Area of a square $= {(side)^2}$---------(1)
Area of a square field $= (89m)$
By substituting the value in equation (1)
Area of a square $= {(side)^2}$$= 89m \times 89m = 7921{m^2}$.
We already know that, $1$ hectare $= 10000{m^2}$.
In our problem, it is asked how many square meters does its area fall, short of a hectare.
Therefore, area remaining to reach $1$ hectare $= 10000 - 7921$ $= 2079$
Area remaining to reach $1$ hectare $= 2079{m^2}$.
By $2079$ square meters its area falls short of a hectare.

Note: All the sides of a square are equal in length.
The area of a square is the product of the length of each side with itself. That is, Area $A = s \times s$, where s is the length of each side of the square. Simply we can say that, area of a square $= {(side)^2}$.
S.I unit of area of square is the metre square (written as $m^2$).