What is a Semicircle?
A semicircle is a geometric shape obtained when a circle is cut into two equal halves
along its diameter. It is called a half circle. Any diameter of a circle cuts the circle into two semicircles.The angle formed by the semi circle is 180 degrees.
Boundary of a semicircle includes one half of the circle boundary and the diameter.
How to use the Semicircle:
Semicircle is used to relate to similar shaped objects and determine the area or perimeter. If r represents the radius and d represents the diameter, then we can write:
Area of a semicircle is half the area of a circle = π/2
Perimeter or circumference is given by πd/2 + d or (π + 2) r
Sample Math Problems
Question
What is the perimeter of a semicircle of radius 10 units?
Answer
Perimeter = π r + 2 r
π(10) + 2(10) = 20 + 10π units
Question
Find the area of a semicircle if the circumference of the circle is 30π units.
Answer
Circumference of circle = 2πr = 30π. So, r = 15 units
Area of semicircle = π/2 = π /2 = 112.5π sq. units
Question
Find the circumference of a semicircle whose area is 24.5π sq units. Take π = 22/7
Answer
Area of semicircle = 24.5π = π/2, So, = 49, r = 7 units
Circumference = (π + 2)r = (22/7+2) 7 = 36 units
Question
Find the area of the shaded region in the design.
Answer
Since the side of the square is 14, the radius of the semicircle is 7 units
Shaded region area = Area of square - Area of 2 semi circles
= Area of square - Area of one circle
= 14 x 14 - π
= 196 - 22/7 (49) = 42 sq units.
