Question

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

Answer 1

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 $m^2$).