Question

Q3. Find the area of shaded region ​

Answer 1

Answer:

GIVEN:

Length of outer rectangle = 26 cm

Breadth of outer rectangle = 12 cm

AREA OF OUTER RECTANGLE = 26 × 12 = 312 cm²

Length of inner region = 26 -(3+3)= 26 -6= 20 cm

Breadth of inner region = 12 -(4+4)= 12 - 8= 4 cm

Breadth of inner rectangle = 4 cm

Diameter of semicircle = Breadth of inner region = 4 cm

Radius of semicircle =  4/2= 2 cm

Height of the semicircle  = Radius of semicircle = 2 cm

Length of inner rectangle = Length of inner region - height of the 2 semicircle

=20 - (2+2) = 20 - 4 = 16 cm

AREA OF INNER RECTANGLE = 16 ×4 = 64 cm²

AREA OF 2 SEMICIRCLES = 2 × ½ πr² = πr²

= π2² = 4π cm²

Area of shaded region = Area of outer rectangle -( area of inner rectangle + Area of 2 semicircles)

Area of shaded region = 312 -(64 +4π)

=312 -64  - 4π = (248 - 4π) cm²

AREA OF SHADED REGION = (248 - 4π) cm²

Hence, the Area of shaded region is (248 - 4π) cm².

HOPE THIS WILL HELP YOU..