Question

in the given figure o is the centre of the circle with AC=24cm, AB=7cm and angle BOD= 90°.fins the area of the shaded region. (Use π = 3.14 and √3 = 1.73205)​

Answer 1

Step-by-step explanation:

Area of the shaded region = area of the circle −area of the triangle ABC−area of the quadrant COD

Here, in triangle ABC ∠CAB=90°

(angle in a semicircle)

Hence triangle ABC is right-angled at A

Then applying Pythagoras theorem,

BC^2 =AC^2 +AB^2

BC^2 =24^2 +7^2

BC^2 =625

BC=25 cm

Therefore diameter of circle =25cm

i.e., Radius= 25/2 =12.5 cm

Then area of circle =πr^2 =490.625 cm^2

Area of ∆ABC = 1/2×base×height =84 cm^2

Area of quadrant = 1/4×πr^2=122.65625 cm^2

Therefore area of shaded region = 490.625−84−122.65625=283.96875 cm^2