Question

Find the area of the shaded region in the given figure, if ABCD is a rectangle with sides 8 cm and 6 cm and O is the centre of the circle.

Answer 1

arrea of the shaded region=area of circle -area of rectangle

$areaofarectangle=l\times b$

$8\times 6=48c{m}^2$

We can get the diagonal of the rectangle by pythagoras theorem which will be the diameter

${hypotenuse}^2=8^2+6^2=64+36=100$

Now

${hypotenuse}^2=100$

$\to \therefore hypotenuse=10cm=equaltothediameter$

so radius =5cm

$areaofcircle=\frac{22}{7}\times 52$

=$\frac{22}{7}\times 25$

$\to =78.57c{m}^2$

area left = area of circle -area of rectangle

area left =78.57-48

$\to 30.57c{m}^2$

$\to \therefore therequiredareais30.57c{m}^2$