The diagnal length of a square is 40 centimeters. Find the area of the square.
+128406 The side will be 40/√2 cm
So......the area = side^2 = ( 40/√2)^2 = 1600/ 2 = 800 cm^2
+26367 The diagnal length of a square is 40 centimeters.
Find the area of the square.
\(\begin{array}{rclrcl} A &=& a^2 \quad & \quad a^2+a^2 &=& 40^2 \\ &&\quad & \quad 2a^2 &=& 40^2 \\ &&\quad & \quad a^2 &=& \frac{40^2}{2} \\ &&\quad & \quad \mathbf{ a } & \mathbf{=} & \mathbf{\frac{40}{\sqrt{2}}} \\ A &=& \left(\frac{40}{\sqrt{2}}\right)^2 \\ A &=& \frac{40^2}{ 2 } \\ \mathbf{ A } & \mathbf{=} & \mathbf{800\ cm^2 } \\ \end{array} \)
