Question

What is the approximate side length of a square game board with an area of $142i{{n}^{2}}$ ?

Answer 1

Hint: To obtain the side of the game board we will use an area of square formula. Firstly we will write the area of the square formula then as we know the value of the area we will substitute it. Finally we will solve the equation obtained to get the desired answer.

Complete step by step solution:
The area of square board game is given as:
Area $=142i{{n}^{2}}$……$\left( 1 \right)$
As we know that area of square is given as:
Area $={{a}^{2}}$……$\left( 2 \right)$
Where,
$a=$ Side of square
Substitute value from equation (1) to equation (2) and simplify as below:
$\begin{align}
  & 142={{a}^{2}} \\
 & \Rightarrow a=\sqrt{142} \\
 & \therefore a\approx 11.916 \\
\end{align}$
So we get $a=11.916in$

Hence side length of a square game board is $11.916in$

Note:
A square is a regular quadrilateral which has four sides and four equal angles of ${{90}^{\circ }}$. It is a closed two-dimensional shape. The diagonal of the square bisects each other and meets at ${{90}^{\circ }}$. The opposite sides of a square are always parallel. The length of all sides is equal. A square is a special case of a rectangle, rhombus, parallelogram and a regular polygon. Area of the square is calculated by multiplying the two sides of it. Perimeter of a square is the sum of all four sides. As we know that the interior angle of a square is ${{90}^{\circ }}$ so we can easily find its diagonal by using Pythagora's theorem. Another example where we find the square shape is a wall clock, a slice of bread and a square photo frame.