Question

A square of side 7 cm is inscribed in a circle. The area of the circle (in cm2) is

Answer 1

Length of Diagonal of the square of side 7cm = 7√2 (Pythagoras theorem)

radius of the circle = (length of diagonal of the inscribed square) / 2 = 7√2/2

Area of the circle = π.r² = π. (7√2/2 )² =  π. 49 × 2 /4 = 22 /7 × 49/2

                      (taking π as 22/7)

=> 77cm²

Answer 2

Answer:

$\bold{77}\ cm^2$

Step-by-step explanation:

$The diameter of the circle is equal to the diagonal of the square. \\ \\ \therefore\ Diameter = 7\sqrt{2}\ cm \\ \\ \ [The diagonal of a square is \sqrt{2}\ times its side.] \\ \\ \\ Radius \ = \frac{7\sqrt{2}}{2}$

$Area \\ \\ = \pi r^2 \\ \\ = \pi \times (\frac{7\sqrt{2}}{2})^2 \\ \\ = \pi \times \frac{98}{4} \\ \\ = \frac{49\pi}{2} \\ \\ = \frac{49}{2} \times \frac{22}{7}\ \ \ \ \ [ Taking \pi\ as \ \frac{22}{7}] \\ \\ = 7 \times 11 = \bold{77}$

$\\ \\ \\ \therefore\ Area \ = \bold{77}\ cm^2$