Introduction
Draw a circle on a piece of paper. Plot the center of the circle. Draw a line through the center of the circle and cut it along the line. We get two plane figures. Each plane figure is bounded by a long curve and a straight line. We could observe that this plane figure is exactly half of the circle. Such plane figure is called as semi circle.
Since plane figure is two dimensional, semi circle possess area and perimeter. We know that angle at the center of the circle is 360 degrees. Angle at the center of the semi circle is half of 360 degrees = 180 degrees.
Choose any point on the circumference of the semi circle and join them to the ends of the diameter of the semi circle. This is a triangle. Angle formed at that point of the triangle is right angle.
Formulas on Semi Circle:
A semicircle has only one diameter.
Area of the semicircle is half of the area of the circle.
Area of semicircle = Area of circle
2
= `(pir^2)/2` sq. units
Circumference of the semi circle = πr units.
If we know the length of the straight line (diameter, d) in the semicircle, then we could find the radius by dividing it with 2.
Circumference of the semicircle if diameter is known = `(pid)/2` units
Perimeter of the semi circle = Circumference of the circle + diameter
= πr + d
= πr + 2r units
Having problem with math test for 6th grade keep reading my upcoming posts, i will try to help you.
Problems on Semicircle Using Formulas:
Ex 1: Find the area, circumference of the semi circle whose diameter is 14 cm.
Sol:
Step 1: Write the given details.
Diameter = 14 cm
Step 2: Find the radius
radius = 14/2 = 7 cm
Step 3: Find the area of the semicircle using the formula
Area of the semi circle = `(pir^2)/2` sq. units
= `22/7 xx 7^2/2`
= 77 cm2
Step 4: Find the circumference of the semi circle
circumference of the semi circle = πr units
= `22/7 xx 7 = 22 cm`
Ex 2: The government has planned to construct a botanical garden in semicircular shape with perimeter of 36 hectare. Calculate the area of the garden.
Sol:
Step 1: Write the given details
Perimeter = 36 cm
Step 2: To find the area, we need radius. So, write the perimeter formula and equate it to 36 and find the radius
πr + 2r= 36
3.14r + 2r = 36
r(3.14 + 2) = 36
5.14r = 36
r = 7.003 = 7 hectare
Step 3: Calculate the area
Area of the semicircle = `(pir^2)/2`
`= 22/7 xx 7^2/2 = 77 ` sq. hectare
Draw a circle on a piece of paper. Plot the center of the circle. Draw a line through the center of the circle and cut it along the line. We get two plane figures. Each plane figure is bounded by a long curve and a straight line. We could observe that this plane figure is exactly half of the circle. Such plane figure is called as semi circle.
Since plane figure is two dimensional, semi circle possess area and perimeter. We know that angle at the center of the circle is 360 degrees. Angle at the center of the semi circle is half of 360 degrees = 180 degrees.
Choose any point on the circumference of the semi circle and join them to the ends of the diameter of the semi circle. This is a triangle. Angle formed at that point of the triangle is right angle.
Formulas on Semi Circle:
A semicircle has only one diameter.
 |
| semi circle |
Area of semicircle = Area of circle
2
= `(pir^2)/2` sq. units
Circumference of the semi circle = πr units.
If we know the length of the straight line (diameter, d) in the semicircle, then we could find the radius by dividing it with 2.
Circumference of the semicircle if diameter is known = `(pid)/2` units
Perimeter of the semi circle = Circumference of the circle + diameter
= πr + d
= πr + 2r units
Having problem with math test for 6th grade keep reading my upcoming posts, i will try to help you.
Problems on Semicircle Using Formulas:
Ex 1: Find the area, circumference of the semi circle whose diameter is 14 cm.
Sol:
Step 1: Write the given details.
Diameter = 14 cm
Step 2: Find the radius
radius = 14/2 = 7 cm
Step 3: Find the area of the semicircle using the formula
Area of the semi circle = `(pir^2)/2` sq. units
= `22/7 xx 7^2/2`
= 77 cm2
Step 4: Find the circumference of the semi circle
circumference of the semi circle = πr units
= `22/7 xx 7 = 22 cm`
Ex 2: The government has planned to construct a botanical garden in semicircular shape with perimeter of 36 hectare. Calculate the area of the garden.
Sol:
Step 1: Write the given details
Perimeter = 36 cm
Step 2: To find the area, we need radius. So, write the perimeter formula and equate it to 36 and find the radius
πr + 2r= 36
3.14r + 2r = 36
r(3.14 + 2) = 36
5.14r = 36
r = 7.003 = 7 hectare
Step 3: Calculate the area
Area of the semicircle = `(pir^2)/2`
`= 22/7 xx 7^2/2 = 77 ` sq. hectare
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