Question

in the fig.,AC=24cm BC=10cm and O is the centre of the circle. find the area of shaded region.

Answer 1

Answer:

Area of shaded region =145.33 cm square

Step-by-step explanation:

It is given that,

,AC=24cm BC=10cm and O is the center of the circle

To find AB

Triangle ABC is a right angled triangle.

$AB=\sqrt{BC^{2}+AC^{2}}$

$AB=\sqrt{10^{2}+24^{2}}$

$AB=\sqrt{100+576}$

$AB=\sqrt{676}$

AB = 26 cm

To find Radius of circle

Radius $r=\frac{AB}{2}$

$r=\frac{26}{2}$

r = 13 cm

To find the area of triangle ABC

Area of right angled triangle =  $\frac{bh}{2}$

$A=\frac{BC*AC}{2}$

$A=\frac{10*24}{2}$

∴ Area of triangle , A₁ = 120 cm square

To find area of semicircle

Area of semi circle is given by

A₂= πr²/2

A₂= (3.14 x 13 x 13)/2 = 265.33

To find area of shaded region

Area of shaded region = A₂ - A₁ =265.33 - 120 = 145.33 cm square

Answer 2

Answer:

Answer:

Area of shaded region =145.33 cm square

Step-by-step explanation:

It is given that,

,AC=24cm BC=10cm and O is the center of the circle

To find AB

Triangle ABC is a right angled triangle.

AB = 26 cm

To find Radius of circle

Radius

r = 13 cm

To find the area of triangle ABC

Area of right angled triangle =  

∴ Area of triangle , A₁ = 120 cm square

To find area of semicircle

Area of semi circle is given by

A₂= πr²/2

A₂= (3.14 x 13 x 13)/2 = 265.33

To find area of shaded region

Area of shaded region = A₂ - A₁ =265.33 - 120 = 145.33 cm square

Step-by-step explanation: