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.

(3 Marks)

Answer 1

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

Area of a rectangle = $l\times b$

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

(1 mark)

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

${hypotenuse}^2=100$

$\to \therefore hypotenuse=10cm$ = equal to the diameter

so radius = 5 cm

(1 mark)

Area of circle = $\frac{22}{7}\times 52$

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

$\to =78.57c{m}^2$ (1 mark)

area left = area of circle -area of rectangle

area left =78.57-48

$\to 30.57c{m}^2$

(1 mark)

$\to \therefore$ the required area is $30.57c{m}^2$