AREA AND PERIMETER OF SEMICIRCLE

Here we are going to see how to find area and perimeter of a semicircle. To understand this topic much better we have given different kinds of example problems.

Semicircle is exactly half the entire circle.

Area of Semi circle  = (1/2)πr² square units

Perimeter of Semi circle = (π + 2)r units

Example 1 :

Find the area of the semicircle whose radius is 7 cm.

Solution :

Area of Semicircle  =  (1/2)πr²

Substitute 7 for r and 22/7 for π. 

=  (1/2) x (22/7) x 7²

=  (1/2) x (22/7) x 7 x 7

=  1 x 11 x 7

=  77 cm²

Example 2 :

Find the area of the semicircle whose radius is 3.5 cm.

Solution :

Area of Semicircle is 

=  (1/2)πr²

Substitute 3.5 for r and 22/7 for π. 

=  (1/2) x (22/7) x 3.5²

=  (1/2) x (22/7) x 3.5 x 3.5

=  19.25 cm²

Example 3 :

Find the circumference of the semicircle whose diameter is 7 cm.

Solution :

Radius (r)  =  Diameter/2

r  =  7/2

r  =  3.5

Circumference of the semicircle is

=  (π + 2)r

Substitute 3.5 for r and 22/7 for π. 

=  (22/7 + 2) x 3.5

=  [(22 + 14) / 7] x 3.5

=  36 x 0.5

=  18 cm

Example 4 :

Find the circumference of the semicircle whose diameter is 42 cm.

Solution :

Radius (r)  =  Diameter/2

r  =  42/2

r  =  21

Circumference of the semicircle is

=  (π + 2)r

Substitute 21 for r and 22/7 for π. 

=  (22/7 + 2) x 21

  =  [(22 + 14) / 7] x 21

=  36 x 3

=  108 cm

Example 5 :

Find the radius of the semicircle whose circumference is 90 cm. 

Solution :

Circumference of the semicircle  =  90 cm

(π + 2)r  =  90

Substitute 22/7 for π. 

(22/7 + 2)r  =  90

[(22 + 14) / 7]r  =  90

(36/7)r  =  90

Multiply each side by 7/36.

r  =  90 x 7/36

r  =  35/2

r  =  17.5 cm

Example 6 :

Find the diameter of the semicircle whose area is  1232 cm². 

Solution :

Area of Semicircle  =  1232 cm²

(1/2)πr²  =  1232

Multiply each side by 2. 

πr²  =  2464

Substitute 22/7 for π. 

(22/7)r²  =  2464

Multiply each side by 7/22.

r²  =  2464 x 7/22

r²  =  784

r²  =  28²

r  =  28 cm

Diameter is

=  2 x r

=  2 x 28

=  56 cm

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