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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