Question

The length of the diagonal of the square is 10 cm. The area of the square is
A. 20 \[c{{m}^{2}}\]
B. 100 \[c{{m}^{2}}\]
C. 50 \[c{{m}^{2}}\]
D. 70 \[c{{m}^{2}}\]

Answer 1

Hint: The length of the two diagonals of the square will be the same. Also, the area of the square when the diagonals length are given, will be given by the formula: \[Area=\dfrac{{{d}^{2}}}{2}\]. Here d is the length of the diagonal of the square.

Complete step-by-step answer:
In the question, we have been given with the length of the diagonal of the square as 10 cm. So, we have to find the area of the square. Now, here we simply know that the two diagonals of the square are equal, as all sides of the square are of the same length. Now, the area formula when the diagonal lengths are given is given by the formula: \[Area=\dfrac{{{d}_{1}}\times {{d}_{2}}}{2}\]. But here since the length of two diagonals of the square are 10 cm so we have: \[{{d}_{1}}={{d}_{2}}=10\,cm\]. So, now the area of the square will be given as follows:
\[\Rightarrow Area=\dfrac{{{d}_{1}}\times {{d}_{1}}}{2}\,\,c{{m}^{2}}\]
Now, since the diagonals area equal so we have \[{{d}_{1}}={{d}_{2}}=10\,cm\], by that we have:
\[\begin{align}
  & \Rightarrow Area=\dfrac{{{d}_{1}}^{2}}{2}\,\,c{{m}^{2}} \\
 & \Rightarrow Area=\dfrac{{{10}^{2}}}{2}\,\,c{{m}^{2}} \\
 & \Rightarrow Area=50\,\,c{{m}^{2}} \\
\end{align}\]
So here the area of the square is 50 \[c{{m}^{2}}\]. Hence, the correct answer is option C) 50 \[c{{m}^{2}}\].

Note: Make sure there is no calculation error while finding \[\dfrac{{{10}^{2}}}{2}\] value. Also, don’t forget to put the unit of area which is \[c{{m}^{2}}\], as the length given is also in cm. Another mistake happens when we take the wrong formula for the area, where we mistakenly take area as\[Area={{d}_{1}}\times {{d}_{2}}\], which is incorrect.