Question

Question 92

Find the area of a square inscribed in a circle whose radius is 7 cm as shown in the figure.

Hint: Four right-angled triangles joined at right angles to form a square.

Answer 1

Given that ABCD is a square.
According to the question.
Area of square ABCD =$4\times$ Area of a right angled triangle
$\therefore$ Area of square $ABCD=4\times$ Area of $\Delta AOB$
$=4\times (\frac{1}{2}\times AO\times BO)$
$[\because$ area of a right angled triangle $=\frac{1}{2}\times base\times height]$
$=2\times 7\times 7=98c{m}^2$
$[\because$ AO = BO = radius of circle = 7 cm, given]
Hence, the area of inscribed square is $98c{m}^2.$