Question

calculate the area of a square whose diagonal is 10 cm. type only the number value in the space to the nearest whole number.

Explanation:

Step1: Relate diagonal to side length

For a square, diagonal $d = s\sqrt{2}$, so solve for side $s$:
$s = \frac{d}{\sqrt{2}} = \frac{10}{\sqrt{2}}$

Step2: Simplify the side length

Rationalize and simplify:
$s = \frac{10\sqrt{2}}{2} = 5\sqrt{2}$

Step3: Calculate area of the square

Area $A = s^2$, substitute $s$:
$A = (5\sqrt{2})^2 = 25 \times 2 = 50$

Answer:

50