Question

In Figure, a square is inscribed in a circle of diameter d and another square is circumscribing the circle. Is the area of the outer square four times the area of the inner square? Give reasons for your answer.

0

• A. True
• B. False

Answer 1

The correct option is B False

Check whether the area of the outer square is four times the area of the inner square or not.

Let the diameter of the circle is $d$.

Diagonal of the inner square $=$Diameter of the circle $=$Side of the outer square.

Side of the square $=\sqrt{\frac{{\mathrm{d}}^2}{2}}$

Area of the inner square $={\left(\mathrm{side}\right)}^2$

$$\begin{gathered} ={\left(\sqrt{\frac{{\mathrm{d}}^2}{2}}\right)}^2 \\ =\frac{{\mathrm{d}}^2}{2} \end{gathered}$$

Area of the outer square $={\left(\mathrm{side}\right)}^2$

$={\mathrm{d}}^2$

We can observe that the area of the outer square is two times the area of the inner square.

Hence, the statement is false